Magnetic phase diagram for a random three-dimensional Ising point-dipole lattice

JETP Letters - It is shown, within the framework of the generalized mean-field theory, that the ground state of a system of Ising point dipoles randomly filling the sites of a three-dimensional...     

Universality classes of Ising models

We discuss a transformation of Ising spins which maps a d-dimentional Ising problem into a series of different problems in the same universality class.     

Universality in Ising model gauge-field analogues

The lattice dependence of a class of gauge-invariant Ising models is investigated. Any lattice dependence would indicate that the lattice could not be regarded as irrelevent and that it would be incorrect to define gauge models on a lattice as a basis for investigating the continuum limit. The models investigated lie within the class of multispin Ising models which show a wide variety of lattice-dependent behaviour and so these models should provide a significant test of the importance of the gauge-invariance constraint. Two and three dimensional models are investigated and lattice independence is confirmed. This indicates that imposing gauge symmetries on lattice models can restrict the possible behaviour in such a way that lattice independent continuum limits can be defined.     

Thermodynamic properties of the site-bond diluted Ising ferromagnet on an anisotropic square lattice

Within the framework of an effective-field theory, we calculate the magnetization, specific heat and susceptibility of a quenched site-bond diluted Ising ferromagnet on a square lattice with both anisotropic coupling constants and anisotropic bond occupancy probabilities. It is shown that these thermodynamic quantities exhibit some interesting behavior as a function of temperature for selected concentrations of magnetic atoms and anisotropic bonds with anisotropic coupling constants.     

Critical properties of the three-dimensional frustrated Ising model on a cubic lattice

The critical properties of the three-dimensional fully frustrated Ising model on a cubic lattice are investigated by the Monte Carlo method. The critical exponents α (heat capacity), γ (susceptibility), β (magnetization), and ν (correlation length), as well as the Fisher exponent η, are calculated in the framework of the finite-size scaling theory. It is demonstrated that the three-dimensional frustrated Ising model on a cubic lattice forms a new universality class of the critical behavior.     

Lower and upper bounds on the critical temperature for anisotropic three-dimensional Ising model

The Ising model is considered on a simple cubic lattice, with a coupling constant J along one axis and coupling constants J’ along the remaining two axes. The transfer-matrix technique and an extended phenomenological renormalization group theory [18, 19] are applied to obtain two-sided bounds on the critical temperature for the model with J′/J≤1. The bounds monotonically converge with decreasing J′/J and provide improved estimates for the phase-transition temperature in anisotropic three-dimensional Ising model, as compared with those available from the literature.     

Monte Carlo study of the Ising antiferromagnetic with a longitudinal field on the anisotropic square lattice

The Ising antiferromagnetic in the presence of a magnetic field on an anisotropic square lattice is studied by Monte Carlo simulation. We obtained the phase diagram in the T-H plane investigating the reentrant behavior around of the critical field Hc=2Jy. Using the Binder cumulant we locate the critical temperature Tc as a function of H. In order to test our simulation, for null field we obtain the critical behavior of Tc as a function of r=Jy/Jx and is in excellent agreement with exact solution of Onsager. Our results indicate a second-order transition for all values of H and particular case r=1 (independent of the ratio r≠0), where not reentrant behavior was observed.     

Universality class of a Fibonacci Ising model

The specific heat of a certain ferromagnetic Fibonacci Ising model is shown to have a logarithmic singularity.     

Universality in finite temperature lattice QCD

In the lattice regularization of QCD, physical results must be independent of the choice of lattice action. Finite temperature thermodynamics provides a very sensitive test of this universality, providing a functional comparison between the predictions of different actions. We study thermodynamics using Wilson's, Manton's and Villain's actions as well as the mixed fundamental-adjoint form of Bhanot and Creutz. Our results support universality in all cases, but indicate that in general the region of couplings in present lattice calculations requires the inclusion of higher order effects in the perturbative solution of the renormalization group equation.     

Bounds for the anisotropic Ising model

Rigorous upper bounds are found for the magnetisation, susceptibility, critical temperature and crossover exponent in an anisotropic Ising system.     

Point defects in the honeycomb Ising lattice

A plane isotropic honeycomb Ising lattice is considered with randomly distributed defects, namely missing lattice spins (including the three adjacent bonds). The impurities are in thermodynamic equilibrium through a chemical potential. We find a rescaled temperature and a finite cusp-like specific heat at the critical point.     

Ising models on the pentagon lattice

We solve inhomogeneous Ising models on the pentagon lattice using the transfer matrix formalism. As two special cases we study the ferromagnetic and the fully frustrated antiferromagnetic model on this lattice. The ferromagnet shows a phase transition at someT _c>0 with the usual Ising behaviour. In the frustrated case no transition occurs at any temperature due to frustration. Frustration also causes a nonvanishing rest entropy. We also calculate the spin-spin-correlation for large distance in both cases. In the ferromagnetic model we thus get the magnetization and the expected algebraic (exponential) decay of the correlations at (above)T _c. The correlations of the frustrated model decay exponentially for all temperatures, includingT=0, indicating that evenT=0 belongs to the disordered high temperature phase. Superimposed to the exponential decay the correlation shows an interesting oscillatory behaviour with temperature dependent wave number, i.e. an incommensurate structure.Work performed within the research program of the Sonderforschungsbereich 125, Aachen-Jülich-Köln     

Universality of the string picture in lattice gauge systems

We test the conjecture that the infrared behaviour of gauge theories is described by an effective string picture by analyzing the Monte Carlo data of five different three- and four-dimensional lattice gauge systems, SU(2) and SU(3) included. We find that there is a unique string of fermionic type which fits well to the whole set of analyzed data.     

Calculation of critical properties for the anisotropic two-layer Ising model on the Kagome lattice: Cellular automata approach

The critical point (K_c) of the two-layer Ising model on the Kagome lattice has been calculated with a high precision, using the probabilistic cellular automata with the Glauber algorithm. The critical point is calculated for different values of the inter- and intra-layer couplings (K₁≠K₂≠K₃≠K_z), where K₁, K₂ and K₃ are the nearest-neighbor interactions within each layer in the 1, 2 and 3 directions, respectively, and K_z is the intralayer coupling. A general ansatz equation for the critical point is given as a function of the inter- and intra-layer interactions, ξ=K₃/K₁,σ=K₂/K₁ and ω=K_z/K₁ for the one- and two-layer Ising models on the Kagome lattice.     

Interface delocalization in the three-dimensional Ising model

The interface delocalization in the three-dimensional Ising model is studied by real-space renormalization group methods. The first-order cumulant expansion approximation is used. Defect free energies for a boundary plane of defects and an internal plane of defects are calculated in the whole temperature region. The phase diagrams are also obtained. The method and the model analyzed may give a correct phase diagram only in the regime of continuous interface delocalization. The interface delocalization is obtained for the boundary defect and also for the internal defect if the systems on two sides of the internal defect plane have a different degree of order. The delocalization transition does not occur in the case of the internal defect plane between two equally ordered systems.     

Ising models on the lattice Sierpinski gasket

Ferromagnetic Ising models on the lattice Sierpinski gasket are considered. We prove the Dobrushin-Shlosmann mixing condition and discuss corresponding properties of the stochastic Ising models.     

Universality and Conformal Invariance for the Ising Model in Domains with Boundary

The partition function with boundary conditions for various two-dimensional Ising models is examined and previously unobserved properties of nonformal invariance and universality are established numerically.