Showing papers in "Journal of Physics A in 1980"
TL;DR: In this paper, a sequence of approximated solutions for the Sherrington-Kirkpatrick model is computed for spin glasses in the new version of the replica theory, in the context of spin glasses.
Abstract: In the framework of the new version of the replica theory, a sequence of approximated solutions is computed for the Sherrington-Kirkpatrick model (see Phys. Rev. Lett., vol.35, p.1972, 1975) of spin glasses.
690 citations
TL;DR: In this article, the breaking of the replica symmetry in spin glasses is studied and it is found that the order parameter is a function on the interval 0-1, and exact results at all the temperatures are in excellent agreement with the computer simulations at zero external magnetic field.
Abstract: The breaking of the replica symmetry in spin glasses is studied. It is found that the order parameter is a function on the interval 0-1. This approach is used to study the Sherrington-Kirkpatrick model. Exact results are obtained near the critical temperature. Approximated results at all the temperatures are in excellent agreement with the computer simulations at zero external magnetic field.
645 citations
TL;DR: In this article, a class of normal ordering representations of quantum operators is introduced, that generalises the Glauber-Sudarshan P-representation by using nondiagonal coherent state projection operators.
Abstract: A class of normal ordering representations of quantum operators is introduced, that generalises the Glauber-Sudarshan P-representation by using nondiagonal coherent state projection operators. These are shown to have practical application to the solution of quantum mechanical master equations. Different representations have different domains of integration, on a complex extension of the usual canonical phase-space. The 'complex P-representation' is the case in which analytic P-functions are defined and normalised on contours in the complex plane. In this case, exact steady-state solutions can often be obtained, even when this is not possible using the Glauber-Sudarshan P-representation. The 'positive P-representation' is the case in which the domain is the whole complex phase-space. In this case the P-function may always be chosen positive, and any Fokker-Planck equation arising can be chosen to have a positive-semidefinite diffusion array. Thus the 'positive P-representation' is a genuine probability distribution. The new representations are especially useful in cases of nonclassical statistics.
491 citations
TL;DR: The hard-hexagon model in lattice statistics (i.e. the triangular lattice gas with nearest-neighbour exclusion) has been solved exactly as mentioned in this paper, and a restricted class of square-lattice models with non-zero diagonal interactions can be solved.
Abstract: The hard-hexagon model in lattice statistics (i.e. the triangular lattice gas with nearest-neighbour exclusion) has been solved exactly. It has a critical point when the activity z has the value 1/2(11+5 square root 5)=11.09017..., with exponents alpha =1/3, beta =1/9. More generally, a restricted class of square-lattice models with nearest-neighbour exclusion and non-zero diagonal interactions can be solved.
458 citations
TL;DR: In this article, the authors employed the Migdal-Kadanoff renormalisation group for two-dimensions to obtain the global phase diagram for the site-bond correlated percolation problem.
Abstract: The Migdal-Kadanoff renormalisation group for two-dimensions is employed to obtain the global phase diagram for the site-bond correlated percolation problem. It is found that the Ising critical point (K=Kc,H=O) is a percolation point for a range of bond probability rho B such that 1>or= rho B>or=1-e-2Kc. In particular, as rho B approaches 1-e-2Kc, the percolation clusters become less compact and coincide with the Ising critical droplets.
412 citations
TL;DR: In this article, a quantum treatment of a coherently driven dispersive cavity is given based on a cubic nonlinearity in the polarisability of the internal medium, which displays bistability and hysteresis in the semiclassical solutions.
Abstract: A quantum treatment of a coherently driven dispersive cavity is given based on a cubic nonlinearity in the polarisability of the internal medium. This system displays bistability and hysteresis in the semiclassical solutions. Quantum fluctuations are included via a Fokker-Planck equation in a generalised P representation. The transmitted light shows a transition from a single-peaked spectrum to a double-peaked spectrum above the threshold of the lower branch. Fluctuations in the field are reduced on the upper branch and both photon bunching and photon antibunching are predicted, for different operating points. An exact solution obtained for the steady-state generalised P function shows decidedly non-equilibrium behaviour, e.g. the lack of a Maxwell construction.
394 citations
TL;DR: When the number of steps in a random walk varies, the distribution of the resultant vector components in the limit of large mean step number may be non-Gaussian as discussed by the authors, and some of its potential applications are reviewed briefly.
Abstract: When the number of steps in a random walk varies, the distribution of the resultant vector components in the limit of large mean step number may be non-Gaussian The statistics and temporal correlation properties of one class of such non-Gaussian limit distributions are derived and some of its potential applications are reviewed briefly
377 citations
TL;DR: In this article, the magnetic properties of spin glasses are studied in a recently proposed mean field theory; in this approach the replica symmetry is broken and the order parameter is a function (q(x)) on the interval 0-1.
Abstract: The magnetic properties of spin glasses are studied in a recently proposed mean field theory; in this approach the replica symmetry is broken and the order parameter is a function (q(x)) on the interval 0-1. Exact results at the critical temperature and approximated results at all the temperatures are derived. The comparison with the computer simulations is briefly presented.
278 citations
TL;DR: In this article, a renormalisation group technique for studying the 2D sine-Gordon theory near its phase transition is presented, where higher order terms in the flow equations beyond those of Kosterlitz (1974) give rise to a new universal quantity; this in turn gives the universal form as well as the relative coefficient of the next-to-leading term in the correlation function of the XY model; the free energy (1PI vacuum sum) is calculated after the singularity at beta 2=4 pi is treated.
Abstract: A systematic renormalisation group technique for studying the 2D sine-Gordon theory (Coulomb gas, XY model) near its phase transition is presented. The new results are (a) higher order terms in the flow equations beyond those of Kosterlitz (1974) give rise to a new universal quantity; (b) this in turn gives the universal form as well as the relative coefficient of the next-to-leading term in the correlation function of the XY model; (c) the free energy (1PI vacuum sum) is calculated after the singularity at beta 2=4 pi is treated; (d) vortices with multiple charges are shown to be irrelevant; (e) symmetry breaking fields are analysed systematically. The main ideas that the sine-Gordon theory can be defined as a double expansion in alpha (fugacity) and delta = beta 2/8 pi -1 (distance from the critical temperature at alpha =0). Wave-function and coupling constant ( alpha ) renormalisations are necessary and sufficient, around beta 2=8 pi where cos phi acquires dimension 2, for functions with elementary SG fields. This gives rise to renormalisation of beta . The renormalisability is proved to the order calculated in the context of the SG theory, and in general, by using the equivalence to the Thirring-Schwinger model. The renormalised beta 2 plays a role analogous to the dimension in a phi 4 theory-8 pi being the critical dimension. beta 2>8 pi gives an infrared asymptotically free theory which leads to the well-known fixed line. The infrared properties are understood by analogy with the non-linear sigma model.
261 citations
TL;DR: Directed bond percolation is shown to be in the same universality class as Reggeon field theory in this paper, and the critical behaviour and critical exponents near the percolations threshold are inferred.
Abstract: Directed bond percolation is shown to be in the same universality class as Reggeon field theory. The critical behaviour and critical exponents near the percolation threshold are thereby inferred.
247 citations
TL;DR: In this article, the authors apply adiabatic regularisation to a scalar field propagating in a Robertson-Walker universe with arbitrary coupling to the scalar curvature.
Abstract: Adiabatic regularisation is applied to a scalar field propagating in a Robertson-Walker universe with arbitrary coupling to the scalar curvature. Explicit expressions for the expectation value of the quantum stress tensor in an adiabatic vacuum are obtained. This calculation yields the terms which are to be subtracted from the divergent mode-sum expressions for expectation values of the stress tensor to give a finite, renormalised stress tensor. It is shown that the removal of the infinite terms in this subtraction procedure corresponds to the renormalisation of coupling constants in Einstein's equation. A short description is given of the way in which adiabatic regularisation produces a trace anomaly.
TL;DR: In this paper, the behavior of weakly charged polyelectrolytes in a poor salt-free solution is considered, using the notion of blobs, and it is shown that in a very dilute solution, where different polyions do not overlap, a transition of the coil-globule type takes place, upon making poorer the thermodynamic quality of the solvent.
Abstract: The behaviour of weakly charged polyelectrolytes in a poor salt-free solution is considered, using the notion of blobs. It is shown that in a very dilute solution, where different polyions do not overlap, a transition of the coil-globule type takes place, upon making poorer the thermodynamic quality of the solvent. This transition occurs in each blob separately. In the region of higher concentrations (the polyions overlap strongly, but the volume fraction occupied by the blobs in the solution is small) an additional effect is predicted: avalanche-type counter-ion condensation. This effect is due to the fact that the polyelectrolyte conformation varies self-consistently, together with the variation of the number of condensed counter ions.
TL;DR: As shown by exact calculations in one dimension and by computer experiments for d=2, the density of the jammed state in the random parking problem tends to its limit value as yd( infinity )-ad tau -1d/, where tau is the time and yd ( infinity ) the final density.
Abstract: As shown by exact calculations in one dimension (d=1) and by computer experiments for d=2, the density of the jammed state in the random parking problem tends to its limit value as yd( infinity )-ad tau -1d/, where tau is the time and yd( infinity ) the final density. The pair correlation function diverges at contact in the final state. Both properties are due to the sure filling of small holes.
TL;DR: In this article, the ground states of a quenched random Ising spin system with variable concentration of mixed nearest-neighbour exchange couplings +or-J on a square lattice are studied by a new method of graph theory.
Abstract: The ground states of a quenched random Ising spin system with variable concentration of mixed nearest-neighbour exchange couplings +or-J on a square lattice (frustration model) are studied by a new method of graph theory. The search for ground states is mapped into the problem of perfect matching of minimum weight in the graph of frustrated plaquettes, a problem which can be solved by the algorithm of Edmonds. A pedestrian presentation of this elaborated algorithm is given with a discussion of the condition of validity.
TL;DR: In this article, the results of a variational renormalisation-group calculation for the magnetic exponent yH of the two-dimensional q-state Potts model suggest a simple relationship between yH and the exactly known critical exponent yT8v of the eight-vertex model.
Abstract: The results of a variational renormalisation-group calculation for the magnetic exponent yH of the two-dimensional q-state Potts model suggest a simple relationship between yH and the exactly known critical exponent yT8v of the eight-vertex model. The relation allows one to predict the critical and tricritical magnetic exponent delta of the q-state Potts model as a function of q.
TL;DR: In this paper, the permanent profile solutions of the continuous classical Heisenberg chain are reviewed and the author expounds on the application of the inverse scattering method, and exhibits the 'diagonal' action angle representation of the model.
Abstract: The permanent profile solutions of the continuous classical Heisenberg chain is reviewed and the author expounds on the application of the inverse scattering method. Extending and amplifying the work of Takhtajan (1977) he exhibits the 'diagonal' action angle representation of the model. The spectrum of the Hamiltonian is exhausted by a magnon band and a soliton band. The magnons have no internal degrees of freedom and can be characterised by the dispersion law E=p2. Like the sine Gordon doublet, the solitons have internal structure, they carry a continuous angular momentum m, and are characterised by the dispersion law E=16 sin2(p/4)/ mod m mod , in accordance with Tjon and Wright (1977). The continuous Heisenberg chain is a completely integrable Hamiltonian system possessing an infinite number of constants of motion. The recursive procedure for the determination of the conserved integrated densities is established.
TL;DR: It is shown that generating function techniques provide an efficient means of enumerating the number of self-avoiding rings (polygons) on the square lattice.
Abstract: It is shown that generating function techniques provide an efficient means of enumerating the number of self-avoiding rings (polygons) on the square lattice. The techniques can be applied to a number of related problems in lattice statistics and statistical mechanics. The enumeration has been extended to polygons of up to 38 steps.
TL;DR: In this article, it was shown that when the change of H(t) is made infinitely slow, the system, when started from a state corresponding to sigma k(0), passes through states corresponding to Sigma j(t), for all t.
Abstract: Let H(t) be a Hamiltonian whose spectrum has for all t a finite number of disjoint components sigma j(t). It is proved that when the change of H(t) is made infinitely slow the system, when started from a state corresponding to sigma k(0), passes through states corresponding to sigma k(t), for all t.
TL;DR: In this article, an extension of the Gibbs equation is presented to extend the range of application of classical irreversible thermodynamics far from equilibrium, and the results are shown to be in agreement with the Boltzmann kinetic theory.
Abstract: In order to extend the range of application of classical irreversible thermodynamics far from equilibrium, an extension of the Gibbs equation is presented. The new Gibbs equation is assumed to contain, besides its usual contributions, supplementary terms equal to the thermodynamic fluxes. The entropy flux and the entropy production also take more general forms than in classical non-equilibrium thermodynamics. As an illustration of the formalism, an isotropic viscous and non-isothermal two-fluid mixture is considered. The results are shown to be in agreement with the Boltzmann kinetic theory.
TL;DR: In this article, an information theoretic approach based on the procedure of maximal entropy is proposed to estimate the probability of an unknown function in terms of partial data, but not limited to the estimation of unknown probabilities, rather, inductive inferences can be drawn regarding the values of general variables.
Abstract: An inversion procedure which provides the most conservative inference for an unknown function in terms of partial data is discussed on the basis of information theoretic considerations. The method is based on the procedure of maximal entropy, but is not limited to the estimation of unknown probabilities. Rather, inductive inferences can be drawn regarding the values of general (if necessary, dimension-bearing) variables. The solution of an inversion problem using data linear in the unknown function is discussed in detail and explicit results are obtained. For every class of problems with common symmetry properties, the general algorithm can be reduced to a more direct procedure. When the data consist of average values for an unknown distribution, the general approach is in the spirit of the Darwin-Fowler method, while the reduced route is the procedure of maximal entropy ('method of most probable distribution') as usually employed in statistical mechanics. Other classes of problems discussed include the representation of an unknown function in a complete orthonormal basis using as input a partial set of expansion coefficients, and the inference of line shapes and power spectra.
TL;DR: In this paper, it has been shown that van Stockum's spacetime is free from singularities and matter at radial infinity below a certain value of the mass per unit length.
Abstract: The solution of van Stockum (1937) consists of a rotating dust interior, and three exterior metrics referring to different ranges of the mass per unit length. It has been stated in the literature that the exterior in static, but it is proved here that this is so only in the low-mass case. An examination of the Riemann tensor shows that van Stockum's spacetime is free from singularities and matter at radial infinity below a certain value of the mass per unit length. The ultrarelativistic case which has closed timelike lines, can occur at physically possible densities and radii.
TL;DR: In this article, effective Hamiltonians for Goldstone modes of the Euclidean group were introduced, representing fluctuations in the surface of a critical droplet or in the interface between two phases.
Abstract: The authors introduce effective Hamiltonians for Goldstone modes of the Euclidean group, representing fluctuations in the surface of a critical droplet or in the interface between two phases. The Euclidean invariance is non-linearly realised on the Goldstone fields. The Hamiltonians are non-renormalisable in more than one dimension, showing that the disappearance of a phase transition in one dimension for systems with a discrete symmetry may be interpreted in terms of the infrared instabilities induced by these modes. The existence and form of these Hamiltonians indicates the universality of the essential singularity at a first-order phase transition in models with Euclidean invariance.
TL;DR: In this paper, the most general spin model with nearest-neighbour interactions invariant under a global Zp symmetry in two dimensions is considered, and the subset of self-dual models is characterised.
Abstract: The most general spin model with nearest-neighbour interactions invariant under a global Zp symmetry in two dimensions is considered. Dual transformations are discussed, and the subset of self-dual models is characterised. The phase diagrams for p>or=5 are particularly rich, containing first-order, second-order and infinite-order phase transitions. In particular, the existence of a massless phase similar to the low-temperature phase of the XY model is established.
TL;DR: In this article, the probability distribution functions between an endpoint and an interior point, and between two interior points, by using exact enumeration to study a lattice self-avoiding walk model, were calculated for a polymer chain in a good solvent.
Abstract: For a polymer chain in a good solvent, the author calculates the probability distribution functions between an endpoint and an interior point, and between two interior points, by using exact enumeration to study a lattice self-avoiding walk model. These distribution functions are different from the usual distribution function between endpoints. At small distance scales, the probability of nearest-neighbour contacts between two interior points is smaller than the probability of contact between two endpoints. FCC and triangular lattices are considered.
TL;DR: In this paper, a self-contained superfield approach to global supersymmetry in anti-de Sitter space (OSp(1,4)) is developed, and the reducibility questions are analyzed, focusing in particular on the structure of chiral representations of OSp(4).
Abstract: A self-contained superfield approach to global supersymmetry in anti-de Sitter space (OSp(1,4)) is developed. General transformation laws for OSp(1,4) superfields are established, and all basic elements of the OSp(1,4)-covariant formalism, such as covariant superfield derivatives, invariant integration measures over the superspace OSp(1,4)/O(1,3) in both the real and shifted bases, relations between different parametrisations of superspace, etc., are given explicitly. The reducibility questions are analysed, focusing in particular on the structure of chiral representations of OSp(1,4). The simplest linear OSp(1,4)-invariant models are constructed: the OSp(1,4) analogue of the Wess-Zumino model and OSp(1,4) extension of the Yang-Mills theory. The first model, together with the spontaneous breaking of OSp(1,4), exhibits an effect of the spontaneous violation of P and CP parties with the strength related to the anti-de Sitter radius. The relation of the proposed approach to supergravity is discussed.
TL;DR: In this paper, it is shown how both the Schrodinger equation and Einstein's equations (with the expectation value of the energy-momentum tensor on the right) can be derived from a variational principle.
Abstract: Discusses the possibility that the non-linear evolution proposed earlier for a relativistic quantum field theory may be related to its coupling to a classical gravitational field. Formally, in the Schrodinger picture, it is shown how both the Schrodinger equation and Einstein's equations (with the expectation value of the energy-momentum tensor on the right) can be derived from a variational principle. This yields a non-linear quantum evolution. Other terms can be added to the action integral to incorporate explicit nonlinearities of the type discussed previously. The authors discuss briefly the possibility of giving a meaning to the resulting equation in a Heisenberg or interaction-like picture.
TL;DR: In this article, the authors studied scalar field theories for which the interaction term of the Hamiltonian is cubic in the fields, and the renormalization group functions for these models were presented up to and including, three-loop contributions, giving critical exponents to order epsilon 3 in 6-epsilon dimensions.
Abstract: The authors study scalar field theories for which the interaction term of the Hamiltonian is cubic in the fields. They indicate the circumstances for which field theory models of this type represent continuous phase transitions. The renormalisation group functions for these models are presented up to, and including, three-loop contributions, giving critical exponents to order epsilon 3 in 6- epsilon dimensions. The exponent sigma which characterises the Yang-Lee edge singularity is given explicitly to this order.
TL;DR: In this paper, the symmetry group of the time-dependent oscillator in N dimensions with equation of motion d2xi/dt2+ Omega 2(t)xi+0, i+1,..., N, gives the full symmetry group SL(N+2, R) of N2+4N+3 operators.
Abstract: The study of the symmetry group of the time-dependent oscillator in N dimensions with equation of motion d2xi/dt2+ Omega 2(t)xi+0, i+1, ..., N, gives the full symmetry group SL(N+2, R) of N2+4N+3 operators. The Noether subgroup consisting of 1/2(N2+3N+6) operators and the resulting constants of motion are given. A table of the commutation relations between the operators gives the structure constants of the associated Lie algebras.
TL;DR: Inhomogeneous differential approximants (J/L;M)f(x), J/L, M, N, N) f(x,y) are defined for functions of one or more variables given as power series expansions, and some of their properties are exposed.
Abstract: Inhomogeneous differential approximants (J/L;M)f(x), (J/L;M,N)f(x,y) etc. are defined for functions of one or more variables given as power series expansions, and some of their properties are exposed. The approximants are easily computable, and numerical studies are reported (for single-variable series) which demonstrate their utility in circumstances where the customary direct or logarithmic derivative Pade approximants (which are limiting cases) are inadequate.
TL;DR: In this article, the authors constructed a B1-type algebra with the aid of an auxiliary angle variable for the Morse oscillator and studied the limit in which the anharmonicity tends to zero.
Abstract: The discrete spectrum for a Morse oscillator is found using an SO(2, 1) algebra. Since this algebra does not prove to be appropriate to compute matrix elements for the oscillator eigenfunctions, the author construct a B1-type algebra with the aid of an auxiliary angle variable. Matrix elements and recurrence relations are found for several useful operators using the algebra. The limit in which the anharmonicity tends to zero is studied.