Showing papers on "Ising model published in 1995"

On the purity of the limiting gibbs state for the Ising model on the Bethe lattice

Abstract: We give a proof that for the Ising model on the Bethe lattice, the limiting Gibbs state with zero effective field (disordered state) persists to be pure for temperature below the ferromagnetic critical temperatureT until the critical temperatureT of the corresponding spin-glass model. This new proof revises the one proposed earlier.

Ising universality in three dimensions: a Monte Carlo study

Abstract: We investigate three Ising models on the simple cubic lattice by means of Monte Carlo methods and finite-size scaling. These models are the spin-1/2 Ising model with nearest-neighbour interactions, a spin-1/2 model with nearest-neighbour and third-neighbour interactions, and a spin-1 model with nearest-neighbour interactions. The results are in accurate agreement with the hypothesis of universality. Analysis of the finite-size scaling behaviour reveals corrections beyond those caused by the leading irrelevant scaling field. We find that the correction-to-scaling amplitudes are strongly dependent on the introduction of further-neighbour interactions or a third spin state. In a spin-1 Ising model, these corrections appear to be very small. This is very helpful for the determination of the universal constants of the Ising model. The renormalization exponents of the Ising model are determined as yt=1.587 (2), yh=2.4815 (15) and yi=-0.82 (6). The universal ratio Q=(m2)2/(m4) is equal to 0.6233 (4) for periodic systems with cubic symmetry. The critical point of the nearest-neighbour spin-1/2 model is Kc=0.2216546 (10).

Density Matrix Renormalization Group Method for 2D Classical Models

Abstract: The density matrix renormalization group (DMRG) method is applied to the interaction round a face (IRF) model. When the transfer matrix is asymmetric, singular-value decomposition of the density matrix is required. A trial numerical calculation is performed on the square lattice Ising model, which is a special case of the IRF model.

Electric-field-dependent dielectric constant and nonlinear susceptibility in srtio3

Abstract: ${\mathrm{SrTiO}}_{3}$ belongs to the class of incipient ferroelectrics in which an electrically ordered state is suppressed by quantum fluctuations. To investigate the nature of these excitations, we have measured the linear and nonlinear susceptibilities of ${\mathrm{SrTiO}}_{3}$ as a function of temperature T and field E. The application of large fields E counteracts the fluctuations and forces the system into an ordered state. The (E,T) diagram is presented. The field dependence of the dielectric constant can be well described within an Ising model including quantum tunneling. Minima in the third harmonic susceptibility, which is a measure of ferroelectric correlations, are taken as evidence for the onset of coherent tunneling phenomena near T=33 K.

Liquid state theories and critical phenomena

Abstract: The description of the critical behaviour within liquid state theories is reviewed with emphasis on both the universal and the non-universal properties. Simple lattice and continuous models, such as the Ising model and the Lennard-Jones fluid, are examined by the use of several techniques, ranging from the integral equation method to the renormalization group analysis. A self-contained derivation of the hierarchical reference theory (HRT) of fluids is given together with a detailed discussion of the universal properties within a simple approximation to the exact HRT equations. Applications to simple models and comparisons with the results of other investigations are presented. HRT is then generalized to binary fluids, allowing for a complete description of the possible critical behaviours in these systems. The problems of a microscopic definition of the order parameter in mixtures and of the origin of strong crossover phenomena in binary fluids are also addressed.

The Spin-Spin Correlation Function in the Two-Dimensional Ising Model in a Magnetic Field at $T=T_c$

Abstract: The form factor bootstrap approach is used to compute the exact contributions in the large distance expansion of the correlation function $ $ of the two-dimensional Ising model in a magnetic field at $T=T_c$. The matrix elements of the magnetization operator $\sigma(x)$ present a rich analytic structure induced by the (multi) scattering processes of the eight massive particles of the model. The spectral representation series has a fast rate of convergence and perfectly agrees with the numerical determination of the correlation function.

Damage spreading and critical exponents for “model A” Ising dynamics

Abstract: Using damage spreading and heat bath dynamics, we study the Ising model in 2 and 3 dimensions with non-conservative dynamics. Our algorithm differs in some important points from previous ones, which makes it rather efficient. We give estimates for the exponent z which seem to be the most precise published so far (2.172 ± 0.006 for d = 2, 2.032 ± 0.004 for d = 3). We also give precise estimates of the exponent θ′ introduced by Janssen et al. (Z. Phys. B 73 (1989) 539) and of analogous but in principle independent exponents. We find surprisingly that some of the latter agree with θ′, and give an explanation for this.

Critical phenomena and quenched disorder

Abstract: Theoretical ideas for deriving singularities of thermodynamical functions at the second-order phase transitions in spin systems with weak quenched disorder are considered. In particular, p-component vector magnets and the two-dimensional Ising model with disorder in spin-spin interactions are studied. Generalisation of the traditional renormalisation-group scheme, which takes into account non-perturbative spin-glass degrees of freedom, is proposed. Low-temperature properties and the phase transition in the Ising systems with quenched random fields are also considered.

An Introduction to the Theory of Spin Glasses and Neural Networks

Abstract: The Ising magnetic systems physics of the spin glass state replica method replica symmetry breaking physics of the replica symmetry breaking replica symmetry breaking solution near Tc ultrametricity scaling in the space of spin glass states experiments partial annealing statistical models of neural networks the Hopfield model partial annealing in neural networks other kinds of neural networks. Appendix: stability of the replica-symmetric solutions.

Exact large deviation bounds up toT c for the Ising model in two dimensions

Abstract: We prove an upper large deviation bound for the block spin magnetization in the 2D Ising model in the phase coexistence region. The precise rate (given by the Wulff construction) is shown to hold true for all β > βc. Combined with the lower bounds derived in [I] those results yield an exact second order large deviation theory up to the critical temperature.

Landau theory of quantum spin glasses of rotors and Ising spins

Abstract: We consider quantum rotors or Ising spins in a transverse field on a d-dimensional lattice, with random, frustrating, short-range, exchange interactions. The quantum dynamics are associated with a finite moment of inertia for the rotors, and with the transverse field for the Ising spins. For a suitable distribution of exchange constants, these models display spin-glass and quantum paramagnet phases and a zero-temperature (T) quantum transition between them. An earlier exact solution for the critical properties of a model with infinite-range interactions cna be reproduced by minimization of a Landau effective-action functional for the model in finite d with short-range interactions. The functional is expressed in terms of a composite spin field which is bilocal in time. The mean-field phase diagram near the T=0 critical point is mapped out as a function of T, strength of the quantum coupling, and applied fields. The spin-glass phase has replica symmetry breaking; but, as in the classical Ising spin glass, the order parameter becomes replica symmetric as T\ensuremath{\rightarrow}0. Next we examine the consequences of fluctuations about the mean field for the critical properties. Above d=8, and with certain restrictions on the values of the Landau couplings, we find that the transition is controlled by a Gaussian fixed point with mean-field critical exponents. For couplings not attracted by the Gaussian fixed point above d=8, and for all physical couplings below d=8, we find runaway renormalization-group flows to strong coupling. General scaling relations that should be valid even at the strong-coupling fixed point are proposed and compared with Monte Carlo simulations.

An overview of the theory of large deviations and applications to statistical mechanics

Abstract: We survey a number of results in the theory of large deviations, including Cramer's Theorem, the Donsker-Varadhan theory, and other modern developments We then apply the large deviation theorems to three models in statistical mechanics, the Curie-Weiss model, the Curie-WeissPotts model, and the Ising model These models are analyzed by the three respective levels of the Donsker-Varadhan theory: the sample means (level 1), the empirical measures (level 2), and the empirical processes and fields (level 3) In the last section a general approach to the large deviation analysis of models in statistical mechanics is formulated

Dynamic Monte Carlo Measurement of Critical Exponents.

Abstract: Based on the scaling relation for the dynamics at the early time, a new method is proposed to measure both the static and dynamic critical exponents. The method is applied to the two-dimensional Ising model. The results are in good agreement with the existing results. Since the measurement is carried out in the initial stage of the relaxation process starting from independent initial configurations, our method is efficient.

Neutron scattering study of the two-dimensional spin S=1/2 square-lattice Heisenberg antiferromagnet Sr2CuO2Cl2

Abstract: We have carried out a neutron scattering investigation of the static structure factorS(q 2D ) (q 2D is the in-plane wave vector) in the two-dimensional spinS=1/2 square-lattice Heisenberg antiferromagnet Sr2CuO2Cl2. For the spin correlation length ξ we find quantitative agreement with Monte Carlo results over a wide range of temperature. The combined Sr2CuO2Cl2-Monte Carlo data, which cover the length scale from ≈1 to 200 lattice constants, are predicted without adjustable parameteres by renormalized classical theory for the quantum nonlinear sigma model. For the structure factor peakS(0), on the other hand, we findS(0)∼ξ 2 for the reduced temperature range 0.16

2D Ising-Like Ferromagnetic Behaviour for the Lamellar Cr2Si2Te6 Compound: A Neutron Scattering Investigation

Abstract: As far as we know, Cr2Si2Te6 is the first compound exhibiting a quasi-2D Ising ferromagnetic behaviour (Tc = 32 K): elastic-neutron-scattering experiments on a single crystal and close examination of the thermal evolution of the order parameter led to the critical exponent β ≈ 0.17, comparable to the expected one for a 2D Ising model (β = 0.125); inelastic-neutron-scattering experiments allowed to determine two magnons dispersion curves with 2D Ising-like character. A third magnetic excitation branch has also been measured, for which a tentative explanation is given.

On Discrete 3-Dimensional Equations Associated with the Local Yang-Baxter Relation

Abstract: The local Yang-Baxter equation (YBE), introduced by Maillet and Nijhoff, is a proper generalization to 3 dimensions of the zero curvature relation. Recently, Korepanov has constructed an infinite set of integrable 3-dimensional lattice models, and has related them to solutions to the local YBE. The simplest Korepanov's model is related to the star-triangle relation in the Ising model. In this paper the corresponding discrete equation is derived. In the continuous limit it leads to a differential 3d equation, which is symmetric with respect to all permutations of the three coordinates. A similar analysis of the star-triangle transformation in electric networks leads to the discrete bilinear equation of Miwa, associated with the BKP hierarchy. Some related operator solutions to the tetrahedron equation are also constructed.

Striped phases in two-dimensional dipolar ferromagnets

Abstract: A uniaxial spin system on the square lattice, where the spins are oriented perpendicular to the lattice and are coupled by both a dipole-dipole interaction and an exchange interaction, is studied. The subtle interplay of the exchange and dipolar interaction in two dimensions destabilizes the ferromagnetic ground state of the nearest-neighbor Ising model and gives rise to a sequence of striped phases. An analytic expression for the leading terms in an asymptotic expansion of the ground-state energy for the striped phase is derived for the discrete lattice. Comparison with the corresponding results for a previously proposed checkerboard state show that the striped phase is the ground state. The results are shown to be in excellent agreement with earlier numerical results. The finite-temperature phase diagram is obtained for a finite lattice using Monte Carlo simulation techniques and the corresponding structure-factor patterns discussed.

Complete analyticity for 2D Ising completed

Abstract: We study the behavior of the two-dimensional nearest neighbor ferromagnetic Ising model under an external magnetic fieldh We extend to every subcritical value of the temperature a result previously proven by Martirosyan at low enough temperature, and which roughly states that for finite systems with — boundary conditions under a positive external field, the boundary effect dominates in the bulk if the linear size of the system is of orderB/h withB small enough, while ifB is large enough, then the external field dominates in the bulk As a consequence we are able to complete the proof that “complete analyticity for nice sets” holds for every value of the temperature and external field in the interior of the uniqueness region in the phase diagram of the model The main tools used are the results and techniques developed to study large deviations for the block magnetization in the absence of the magnetic field, and recently extended to all temperatures below the critical one by Ioffe

Monte Carlo simulation of phase transitions in a two-dimensional random-bond Potts model.

Abstract: Using the ``multihit'' Swendsen-Wang cluster flipping method, we performed extensive Monte Carlo simulations to investigate the critical behavior of the two-dimensional (2D) eight-state random-bond Potts model. We applied finite-size-scaling techniques to extract the critical exponents for two different sets of bond strengths, from which we concluded that the transition is second order with critical exponents for both sets falling into same universality class, that of a 2D Ising model. A variation of the Lee-Kosterlitz method for determining the order of a phase transition was also applied. The double-peaked structure of the specific heat, which was found in some of the bond configurations, was also studied by simulation on periodic arrangements of strong and weak bonds.

Monte Carlo method for spin models with long-range interactions

Abstract: We introduce a Monte Carlo method for the simulation of spin models with ferromagnetic long-range interactions in which the amount of time per spin-flip operation is independent of the system size, in spite of the fact that the interactions between each spin and all other spins are taken into account. We work out two algorithms for the q-state Potts model and discuss the generalization to systems with other interactions and to O(n) models. We illustrate the method with a simulation of the mean-field Ising model, for which we have also analytically calculated the leading finite-size correction to the dimensionless amplitude ratio 2/ at the critical temperature.

Ferrimagnetism in diluted mixed Ising spin systems.

Abstract: The magnetic properties of diluted mixed Ising ferrimagnetic systems consisting of spin-1/2 and spin-1 are investigated within the framework of an effective-field theory with correlations. Particular emphasis is given to the honeycomb lattice with coordination number z=3 for which the phase diagram (transition temperature and compensation temperature) and magnetizations (total and sublattice) are obtained. We find a number of interesting phenomena in these quantities, such as the possibility of two compensation points in the total magnetization curve and magnetization curves not predicted in the N\'eel theory.

Dynamics of the Magnetization with an Inversion of the Magnetic Field

Abstract: Time dependence of a magnetization under a time dependent magnetic field in systems with quantum fluctuations is studied by a direct numerical method. In particular, the time evolution of a system under a reversing field is investigated. Even a system has metastability, system can relax to the stable state when the field changes slowly enough. The process is found to be understood through the Landau-Zener mechanism. The change of the state from a metastable state is discussed in the light of quantum tunneling.

Exact Five-Loop Renormalization Group Functions of $\phi^4$-Theory with O(N)-Symmetric and Cubic Interactions. Critical Exponents up to $\ep^5$

Abstract: The renormalization group functions are calculated in $D=4-\epsilon$ dimensions for the $\phi^4$-theory with two coupling constants associated with an ${O}(N)$-symmetric and a cubic interaction. Divergences are removed by minimal subtraction. The critical exponents $\eta$, $ u$, and $\omega$ are expanded up to order $\epsilon^5$ for the three nontrivial fixed points O(N)-symmetric, Ising, and cubic. The results suggest the stability of the cubic fixed point for $N\geq3$, implying that the critical exponents seen in the magnetic transition of three-dimensional cubic crystals are of the cubic universality class. This is in contrast to earlier three-loop results which gave $N > 3$, and thus Heisenberg exponents. The numerical differences, however, are less than a percent making an experimental distinction of the universality classes very difficult.

A Simple Ising-Like Model for Spin Conversion Including Molecular Vibrations

Abstract: An Ising-type model for spin conversion, explicitly accounting for intramolecular vibrations has been studied. Each two level system is associated with p harmonic oscillators having two possible frequencies ω LS (i) , ω HS (i) . The major advantage of this model is that it provides an excellent agreement with both the conversion curve and calorimetric data, in particular the entropy change upon spin conversion. With the help of Arrhenius plots, the predictions of the model are accurately compared to the literature experimental data on the spin equilibrium curves. A very accurate Mossbauer investigation by Jacobi, Spiering and Gutlich, provides evidence for a small effect typical for vibrations. A novel example is given where the conversion curve is essentially monitored by vibrations; this originates from the extremely small value of the energy gap between HS and LS electrovibrational groundstates. However, in most cases, as a first approach, the low frequency approximation of the model can be used. Then the model reduces to a simple two-level model with additional degeneracies implicitely accounting for intramolecular vibrations