Showing papers on "Ising model published in 1990"

Magnetic properties of layered transition metal compounds

Abstract: to Low-Dimensional Magnetic Systems.- 1. Experimental realizations of 2-d magnetic systems.- 2. Magnetic model Hamiltonians.- 3. Survey of the predicted magnetic behaviour.- 4. Lattice- and spin-dimensionality crossovers in quasi 2-d magnetic systems.- 5. Magnetic and nonmagnetic impurity doping in quasi 2-d magnets.- References.- Theory of Two-Dimensional Magnets.- 1. Introduction.- 2. Ising magnets.- 2.1. Ising model. Excitations and phase transitions.- 2.2. Onsager solution.- 2.3. Critical exponents and scaling.- 2.4. Dual transformation. Order and disorder.- 3. Planar magnets.- 3.1. XY model.- 3.2. Excitations.- 3.3. Scaling and correlations.- 3.4. Phase transition.- 3.5. Magnetic vortices as a Coulomb gas.- 3.6. Relationships with other models.- 3.7. Planar antiferromagnets.- 4. Heisenberg magnets.- 4.1. Heisenberg model and real magnets.- 4.2. Renormailzation of the temperature.- 4.3. Heisenberg ferromagnets in an external magnetic field.- 4.4. Excitations of the 2-d Heisenberg model.- 4.5. Dipolar interactions.- 5. Experimental layered magnets.- 5.1. Ising layered magnets. ANNNI model: application to CeSb and CeBi.- 5.2. Layered planar magnets.- 5.3. Layered Heisenberg magnets.- 6. Dynamics of 2-d magnets.- 6.1. Equations of motion.- 6.2. Spin-wave dynamics.- 6.3. Spin-diffusion dynamics.- 6.4. Dynamics of localized excitations.- 6.5. Resonant paramagnetic cxcitation of vortex pairs.- 6.6. Summary.- Acknowledgement.- References.- Application of High- and Low-Temperature Series Expansions to Two-Dimensional Magnetic Systems.- 1. Introduction.- 1.1. Series expansions.- 1.2. Methods applied in series analysis.- 1.2.1. Ratio methods.- 1.2.2. Pade approximant methods.- 1.2.3. Other methods of series analysis.- 2. Series expansions and predictions for the 2-d Ising model.- 2.1. Spin 1/2 model with nearest neighbours only (simple 2-d lattices).- 2.1.1. High-temperature series.- 2.1.2. Low-temperature series.- 2.1.3. Properties in nonzero parallel field.- 2.1.4. Properties in nonzero perpendicular field.- 2.2. Ising model with general S.- 2.3. Other series for I (1/2).- 2.3.1. Restricted dimensionality systems.- 2.3.2. Further-neighbour interactions.- 2.3.3. Crossover from 2-d to 3-d behaviour.- 3. Series expansions and predictions for the Heisenberg model.- 3.1. Series for S = 1/2, arbitrary S and S = ?.- 3.1.1. Properties at nonzero field.- 3.2. Other series for the Heisenberg model.- 3.2.1. Restricted dimensionality.- 3.2.2. Further-neighbour interactions.- 3.2.3. Crossover from 2-d to 3-d behaviour.- 4. Series expansion in the X Y and Ising-to Low-Dimensional Magnetic Systems.- 1. Experimental realizations of 2-d magnetic systems.- 2. Magnetic model Hamiltonians.- 3. Survey of the predicted magnetic behaviour.- 4. Lattice- and spin-dimensionality crossovers in quasi 2-d magnetic systems.- 5. Magnetic and nonmagnetic impurity doping in quasi 2-d magnets.- References.- Theory of Two-Dimensional Magnets.- 1. Introduction.- 2. Ising magnets.- 2.1. Ising model. Excitations and phase transitions.- 2.2. Onsager solution.- 2.3. Critical exponents and scaling.- 2.4. Dual transformation. Order and disorder.- 3. Planar magnets.- 3.1. XY model.- 3.2. Excitations.- 3.3. Scaling and correlations.- 3.4. Phase transition.- 3.5. Magnetic vortices as a Coulomb gas.- 3.6. Relationships with other models.- 3.7. Planar antiferromagnets.- 4. Heisenberg magnets.- 4.1. Heisenberg model and real magnets.- 4.2. Renormailzation of the temperature.- 4.3. Heisenberg ferromagnets in an external magnetic field.- 4.4. Excitations of the 2-d Heisenberg model.- 4.5. Dipolar interactions.- 5. Experimental layered magnets.- 5.1. Ising layered magnets. ANNNI model: application to CeSb and CeBi.- 5.2. Layered planar magnets.- 5.3. Layered Heisenberg magnets.- 6. Dynamics of 2-d magnets.- 6.1. Equations of motion.- 6.2. Spin-wave dynamics.- 6.3. Spin-diffusion dynamics.- 6.4. Dynamics of localized excitations.- 6.5. Resonant paramagnetic cxcitation of vortex pairs.- 6.6. Summary.- Acknowledgement.- References.- Application of High- and Low-Temperature Series Expansions to Two-Dimensional Magnetic Systems.- 1. Introduction.- 1.1. Series expansions.- 1.2. Methods applied in series analysis.- 1.2.1. Ratio methods.- 1.2.2. Pade approximant methods.- 1.2.3. Other methods of series analysis.- 2. Series expansions and predictions for the 2-d Ising model.- 2.1. Spin 1/2 model with nearest neighbours only (simple 2-d lattices).- 2.1.1. High-temperature series.- 2.1.2. Low-temperature series.- 2.1.3. Properties in nonzero parallel field.- 2.1.4. Properties in nonzero perpendicular field.- 2.2. Ising model with general S.- 2.3. Other series for I (1/2).- 2.3.1. Restricted dimensionality systems.- 2.3.2. Further-neighbour interactions.- 2.3.3. Crossover from 2-d to 3-d behaviour.- 3. Series expansions and predictions for the Heisenberg model.- 3.1. Series for S = 1/2, arbitrary S and S = ?.- 3.1.1. Properties at nonzero field.- 3.2. Other series for the Heisenberg model.- 3.2.1. Restricted dimensionality.- 3.2.2. Further-neighbour interactions.- 3.2.3. Crossover from 2-d to 3-d behaviour.- 4. Series expansion in the X Y and Ising-Heisenberg models.- 4.1. Series for the 2-d XY model.- 4.2. Series for the 2-d Ising-Heisenberg model.- 5. Applications to magnetic systems.- 5.1. Ising model.- 5.2. Heisenberg model.- 5.2.1. Spin 1/2.- 5.2.2. Spin 1.- 5.2.3. Spin 3/2 and spin 2.- 5.2.4. Spin 5/2.- 5.2.5. Restricted dimensionality.- 5.3. XY and Ising-Heisenberg models.- Acknowledgements.- References.- Spin Waves in Two-Dimensional Magnetic Systems: Theory and Applications.- 1. Introduction.- 2. Magnetic structures and spin Hamiltonians.- 3. Spin wave theory of model systems.- 4. Dispersion relation.- 5. Thermodynamic properties.- 6. Impurities in antiferromagnets.- References.- Neutron Scattering Experiments on Two-Dimensional Heisenberg and Ising Magnets.- 1. Introduction.- 2. 2-d systems with Ising and Heisenberg interactions.- 2.1. K2CoF4: a 2-d Ising system.- 2.2. K2FeF4: a 2-d planar antiferromagnet.- 2.3. K2MnF4 and K2NiF4: weakly anisotropic Heisenberg magnets.- 2.4. Rb2CrCl4: a planar Heisenberg ferromagnet with small anisotropy.- 2.5. K2CuF4: a planar Heisenberg ferromagnet.- 3. 2-d random magnetic systems.- 3.1. Phase transitions and critical phenomena.- 3.2. Excitations.- 3.3. Random field effects.- 3.4. Relaxation front 2-d to 3-d order.- 3.5. Competing anisotropics and interactions.- 4. Triangular lattice antiferromagnet (TALAF).- 4.1. Fluctuations.- 4.2. An additional degree of freedom.- 4.3. Perturbation.- 4.4. Quantum effect RbFeCl3 and CsFeCl3 VX2 (X = Cl, Br, I) AMX2 (A = Li, Na, K M = 3d metal ion X = O, S, Se).- References.- Phase Transitions in Quasi Two-Dimensional Planar Magnets.- 1. Introduction.- 2. Phase transition and excitations in the 2-d XY model.- 3. Crystallographic properties of BaM2(X)4)2 compounds.- 4. Magnetic properties of BaNi2(PO4)2.- 4.1. Static properties.- 4.2. Dynamic properties.- 4.3. Critical properties.- 5. Magnetic properties of BaCo2(AsO4)2.- 5.1. Static properties.- 5.2. Magnetic phase diagrams.- 5.3. Dynamic properties.- 6. Magnetic properties of BaNi2(AsO4)2.- 6.1. Static properties.- 6.2. Dynamic properties.- 7. Magnetic properties of BaCo2(PO4)2.- 8. Other experimental realizations of the 2-d planar model.- 8.1. K2CuF4.- 8.2. NiCl2 and CoCL2 graphite intercalated compounds NiCl2-GIC CoCl2-GIC.- 9. Concluding remarks.- Acknowledgement.- References.- Spin Dynamics in the Paramagnetic Regime: NMR and EPR in Two-Dimensional Magnets.- 1. Introduction.- 1.1. Dynamics of the 2-spin correlation functions.- 1.2. Nuclear magnetic resonance (NMR).- 1.3. Electron paramagnetic resonance (EPR).- 2. General formalism.- 2.1. Diffusion and dimensionality.- 2.2. Cut-off and EPR linewidth.- 3. EPR spectrum.- 3.1. Diffusion of 4-spin correlation functions.- 3.2. Secular contribution D0.- 3.3. Nonsecular contributions.- 3.4. Satellite line.- 4. Experiments on quasi 2-d Heisenberg magnets.- 4.1. NMR experiments.- 4.2. EPR experiments.- 4.2.1. Angular dependence of linewidth.- 4.2.2. Frequency dependence of magic angle linewidth.- 4.2.3. Dynamic shift.- 4.2.4. Lineshape of the main line.- 4.2.5. Satellite lines at half resonance field.- 5. Critical dynamcis.- 5.1. Critical behaviour of the NMR line.- 5.1.1. Isotropic regime.- 5.1.2. Anisotropic regime.- 5.1.3. Experiments.- 5.2. Critical behaviour of the EPR linewidth.- 5.2.1. Ferromagnets.- 5.2.2. Antiferromagnets.- 5.3. AC susceptibility.- 6. Conclusions.- References.- Field-Induced Phenomena in Two-Dimensional Weakly Anisotropic Heisenberg Antiferromagnets.- 1. Introduction.- 2. Effective, field-dependent anisotropies.- 3. The phase diagram.- 4. Random fields and domain walls (solitons).- 5. The spin flop transition.- 6. The bicritical point.- 7. Concluding remarks.- Acknowledgements.- References.- Index of Names.- Index of Chemical Compounds.- Index of Subjects.

Twisted boundary conditions and effective mass in Heisenberg-Ising and Hubbard rings.

Abstract: We identify the boundary energy of a many-body system of fermions on a lattice under twisted boundary conditions as the inverse of the effective charge-carrying mass, or the stiffness, renormalizing nontrivially under interactions due to the absence of Galilean invariance. We point out that this quantity is a sensitive and direct probe of the metal-insulator transitions possible in these systems, i.e., the Mott-Hubbard transition or Density-wave formation. We calculate exactly the stiffness, or the effective mass, in the 1D Heisenberg-Ising ring and the 1D Hubbard model by using the ansatz of Bethe. For the Hubbard ring we also calculate a spin stiffness by extending the nested ansatz of Bethe-Yang to this case.

Rounding effects of quenched randomness on first-order phase transitions

Abstract: Frozen-in disorder in an otherwise homogeneous system, is modeled by interaction terms with random coefficients, given by independent random variables with a translation-invariant distribution. For such systems, it is proven that ind=2 dimensions there can be no first-order phase transition associated with discontinuities in the thermal average of a quantity coupled to the randomized parameter. Discontinuities which would amount to a continuous symmetry breaking, in systems which are (stochastically) invariant under the action of a continuous subgroup ofO(N), are suppressed by the randomness in dimensionsd≦4. Specific implications are found in the Random-Field Ising Model, for which we conclude that ind=2 dimensions at all (β,h) the Gibbs state is unique for almost all field configurations, and in the Random-Bond Potts Model where the general phenomenon is manifested in the vanishing of the latent heat at the transition point. The results are explained by the argument of Imry and Ma [1]. The proofs involve the analysis of fluctuations of free energy differences, which are shown (using martingale techniques) to be Gaussian on the suitable scale.

Ising transition in frustrated Heisenberg models.

Abstract: We derive scaling equations for a 2D square Heisenberg model where frustration spontaneously breaks the {ital Z}{sub 4} lattice symmetry. At short distances, the model behaves as two interpenetrating Neel sublattices. Short-wavelength fluctuations couple these sublattices, driving a crossover to single-lattice behavior at long distances and generating an Ising order parameter. When the spin-correlation and crossover lengths become comparable, there exists a finite-temperature Ising phase transition {ital independent} of the subsequent development of a sublattice magnetization.

Dynamic phase transition in the kinetic Ising model under a time-dependent oscillating field

Abstract: We analyze within a mean-field approach the stationary states of the kinetic Ising model described by the Glauber stochastic dynamics and subject to a time-dependent oscillating external field We have found that the magnetization of the system oscillates in time around a certain value that is zero at high temperatures or large field amplitudes and nonzero at low temperatures and small field amplitudes The transition from one regime to the other, which corresponds to a spontaneous symmetry breaking, is found to be continuous for sufficiently small values of the field amplitudes For higher values the transition becomes discontinuous and the system exhibits a dynamical tricritical point

Nonperturbative solution of the Ising model on a random surface.

Abstract: The two-matrix-model representation of the Ising model on a random surface is solved exactly to all orders in the genus expansion. The partition function obeys a fourth-order nonlinear differential equation as a function of the string coupling constant. This equation differs from that derived for the k=3 multicritical one-matrix model, thus disproving that this model describes the Ising model. A similar equation is derived for the Yang-Lee edge singularity on a random surface, and is shown to agree with the k=3 multicritical one-matrix model.

New numerical method to study phase transitions.

Abstract: A powerful method of detecting first order transitions by numerical simulations of finite systems is presented. The method relies on simulations and the finite size scaling properties of free energy barriers between coexisting states. It is demonstrated that the first order transitions in d = 2, q = 5 and d = q = 3 Potts models are easily seen with modest computing time. The method can also be used to obtain quite accurate estimates of critical exponents by studying the barriers in the vicinity of a critical point. Some new results on exponents and conformal charge in frustrated XY models and a related coupled XY-Ising model in d = 2 are presented. These show that the transitions in these models are in new universality classes and that the conformal charge varies with a parameter.

Field-theoretical approach to critical phenomena.

Abstract: The study of the Wegner-Houghton equation in the local-potential approximation yields infrared-stable renormalization-group trajectories that are rejected by field theory. The most stable one corresponds to an approach to the infrared-stable fixed point from the unusual side, yielding negative correction-to-scaling amplitudes as already observed in a binary mixture. We also show how this affects the analysis made by Baker and Kincaid, who concluded that the field-theoretic framework fails in describing the critical behavior of the spin-(1/2 Ising model at d=3.

The gas-liquid transition of the two-dimensional Lennard-Jones fluid

Abstract: Monte Carlo simulations of two-dimensional fluids with a truncated Lennard-Jones interaction in the NVT ensemble are analysed with a block density distribution technique, for N=256 and N=576 particles. It is shown that below Tc (critical temperature) the block density function develops a well defined two-peak structure. From the locations of these two peaks the densities of the two coexisting phases can be reliably estimated. In the one-phase region the width of the single-peak is used to extract information on the compressibility, by extrapolating the results for finite block size versus inverse block linear dimension to the thermodynamic limit. Studying the temperature dependence of the fourth-order cumulant of the block density distribution at the critical density for various block sizes, the location of the critical temperature is found from the intersection of the cumulants, just as in the simpler case of Ising models. The authors' results suggest that finite-size scaling techniques can be used to analyse the critical properties of Lennard-Jones fluids and related systems.

Ising model in a time-dependent magnetic field.

Abstract: We report the results of Monte Carlo simulations on a two-dimensional Ising model in a sinusoidally oscillating external magnetic field. We find evidence for a dynamical phase transition, supporting the results of recent mean-field and large-N analyses of this model. We also analyze the hysteresis loops as a function of the amplitude and frequency of the applied field, fitting our data to a proposed areal scaling law.

Conformal field theory and purely elastic s-matrices

Abstract: Particular perturbations of a 2D Conformal Field Theory leading to Integrable massive Quantum Field Theories are examined. The mass spectra and S-matrices for some models, including the field theory of the Ising Model with magnetic field and “thermal” deformations of the tricritical Ising and 3-state Potts models, are proposed. The hidden Lie-algebraic structures of these spectra and their relation to the Toda systems are discussed.

Finite-size effects in fluid interfaces

Abstract: Finite-size effects in interfacial tensions of fluid interfaces are studied at the level of the Gaussian model of capillary waves. It had been suggested that such effects might play a significant role in surface tension measurements based on capillary rise between plates spaced a small distance D apart, the finite-size correction varying as 1/ D . A reconsideration of the thermodynamics of finite-size effects, followed by careful calculations for the Gaussian model, leads to a finite-size correction varying as 1/ D 2 , with a universal coefficient; the effect is too small to be noticeable in current experiments. The calculations have been carried out for rectangular interfaces of arbitrary dimensionality and general shapes subject to many types of boundary conditions. They also have implications for finite-size effects in interfacial free energies in two- and three-dimensional Ising models, which are discussed in connection with recent exact and Monte Carlo calculations.

Dipolar magnets and glasses: Neutron-scattering, dynamical, and calorimetric studies of randomly distributed Ising spins.

Abstract: We have measured the magnetic correlations, susceptibility, specific heat, and thermal relaxation in the dipolar-coupled Ising system LiHo_xY_(1-x)F_4. The material is ferromagnetic for spin concentrations at least as low as x=0.46, with a Curie temperature obeying mean-field scaling relative to that of pure LiHoF_4. In contrast, an x=0.167 sample behaves as a spin glass above its transition temperature, while an x=0.045 crystal shows very different glassy properties characterized by decreasing barriers to relaxation and nonexponential thermal relaxation as T→0. We find the properties of the x=0.045 system to be consistent with a single low-degeneracy ground state with a large gap for excitations. The x=0.167 sample, however, supports a complex ground state with no appreciable gap, in accordance with prevailing theories of spin glasses. The underlying causes of such disparate behavior are discussed in terms of random clusters as probed by neutron studies of the x=0.167 sample.

Solvable model of the quantum spin glass in a transverse field.

Abstract: The spin-glass model with p-spin interactions in the presence of a transverse field is solved in the limit p\ensuremath{\rightarrow}\ensuremath{\infty}. The phase diagram is obtained and consists of three phases: A spin-glass phase and two paramagnetic phases. The paramagnetic phases are distinguished by transverse ordering. The spin-glass phase is similar to that of the random-energy model.

The critical behaviour of the two-dimensional dilute Ising magnet

Abstract: Two-dimensional random-bond Ising models of L × L spins are simulated extensively. In the randomness dominated critical region, the size dependences of the specific heat, C , the susceptibility, χ, and the magnetization, m , at critically are in very good agreement with the analytic predictions, C ≈ ln ln L , χ ≈ L if 7 4 , and m ≈ L −1 8 . The temperature dependences of χ and m close to the critical point can be described by power laws with the exponents of the perfect model, modified by logarithmic corrections.

Phase transitions in surface segregation of PtcNi1-c alloys from tight-binding Ising-model calculations.

Abstract: The tight-binding Ising model coupled with a mean-field approximation formulated as an area-preserving map is applied to surface segregation of Pt{sub {ital c}}Ni{sub 1{minus}{ital c}} alloys. It allows us to reproduce the striking experimental data available for the low-index faces and in particular the face-related segregation reversal observed when going from the (111) to the (110) face. Moreover, it predicts some spectacular phase transitions of the concentration profiles as a function of temperature and bulk concentration.

Perturbation expansions for quantum many-body systems

Abstract: A systematic method for developing high-order, zero-temperature perturbation expansions for quantum many-body systems is presented. The models discussed explicitly are spin models with a variety of interactions, in one and two dimensions. The wide applicability of the method is illustrated by expansions around Hamiltonians with ordered and disordered ground states, namely Ising and dimerized models. Computer implementation of this method is discussed in great detail. Some previously unpublished series are tabulated.

Ising spin glass in a transverse field: Replica-symmetry-breaking solution.

Abstract: The replica-symmetry-breaking (RSB) solution of the infinite-range Ising spin glass in the presence of a transverse field is obtained. The quenched free energy and the phase boundary of the glass transition temperature versus the transverse field are calculated at first-step RSB without using the static approximation. We demonstrate that replica symmetry (RS) has to be broken in the spin-glass phase by comparing the free energies of the RSB and RS solutions. No evidence is found to support an intermediate spin-glass phase with replica symmetry