Phase diagram of the antiferromagnetic triangular Ising model with anisotropic interactions

It is argued that there exist two antiferromagnetic phases in the triangular Ising model with anisotropic interactions. A method due to Müller-Hartmann and Zittartz (MZ) is used to derive a closed-form expression for the phase boundary. We also give a criterion under which the MZ method is expected to be applicable and accurate.Work supported in part by a grant from the National Science Foundation.     

Yang-Lee zeros of the antiferromagnetic Ising model

There exists the famous circle theorem on the Yang-Lee zeros of the ferromagnetic Ising model. However, the Yang-Lee zeros of the antiferromagnetic Ising model are much less well understood than those of the ferromagnetic model. The precise distribution of the Yang-Lee zeros of the antiferromagnetic Ising model only with nearest-neighbor interaction J on LxL square lattices is determined as a function of temperature a=e(2betaJ) (J<0), and its relation to the phase transitions is investigated. In the thermodynamic limit (L-->infinity), the distribution of the Yang-Lee zeros of the antiferromagnetic Ising model cuts the positive real axis in the complex x=e(-2betaH) plane, resulting in the critical magnetic field +/-H(c)(a), where H(c)>0 below the critical temperature a(c)=square root of 2-1. The results suggest that the value of the scaling exponent y(h) is 1 along the critical line for a相似文献   

Bethe-Peierls approximation for the disordered Ising model

We study the Ising model for an alloy with an arbitrary number of components. We develop an approximation which reduces to that of Bethe and Peierls when the concentration of one of the components is unity. We investigate within this approximation the dependence of the various thermodynamic quantities, in particularT _c, on the composition of the alloy and the magnetic properties of its constituents. Comparison with the only exact calculation available, that of F. T. Leeet al., for a linear chain, shows extremely satisfactory agreement.Research supported by ARO (D). It has also benefited from the general support of Materials Science at the University of Chicago by the NSF.     

Analyticity properties of the Ising model in the antiferromagnetic phase

The partition function of the Ising antiferromagnet is proved to have no zeroes in an annulus around the origin in the complexz-plane. The intersection of this annulus with the positive real axis belongs to the antiferromagnetic region. The free energy and the correlation functions are analytic in the annulus.On leave of absence from the University of Groningen, the Netherlands; supported by the Netherlands Organization for Pure Scientific Research (Z.W.O.).Supported by the National Swiss Foundation for Scientific Research.     

Dynamics of antiferromagnetic Ising model with fixed magnetization

The dynamical critical exponent z of the Ising antiferromagnet under the constraint of a fixed zero magnetization is verified by Monte Carlo simulations to be compatible with that of the usual Glauber dynamics of model A, while for positive magnetization the exponent seems different. We also determine the diffusivity of the magnetization and finite size effects. Received: 18 June 1997 / Revised: 28 July 1997 / Accepted: 13 October 1997     

The antiferromagnetic Ising model for a bilayer Bethe lattice

The totally antiferromagnetic Ising model is analyzed on a bilayer Bethe lattice in detail by studying the order-parameters, response functions, i.e. susceptibility and specific heat, and free energy by using the recursion relations in a pairwise approach. The ground state phase diagrams of the model are also obtained on the (_J2/|_J1|,_J3/q|_J1|)$(J_2/|J_1|,J_3/q|J_1|)$ plane for given values of H/q|_J1|$H/q\left|J_1\right|$ and on the (H/q|_J1|,_J3/q|_J1|)$(H/q|J_1|,J_3/q|J_1|)$ plane for given _J2/|_J1|$J_2/\left|J_1\right|$. As a result, we have obtained the temperature-dependent phase diagrams for various values of the coordination number q   on the (_J3/|_J1|,kT/|_J1|)$(J_3/|J_1|,\mathit{kT}/|J_1|)$ and (H/|_J1|,kT/|_J1|)$(H/|J_1|,\mathit{kT}/|J_1|)$ planes for given values of the rest of the system parameters.     

Analysis of a long-range random field quantum antiferromagnetic Ising model

We introduce a solvable quantum antiferromagnetic model. The model, with Ising spins in a transverse field, has infinite range antiferromagnetic interactions and random fields on each site following an arbitrary distribution. As is well-known, frustration in the random field Ising model gives rise to a many valley structure in the spin-configuration space. In addition, the antiferromagnetism also induces a regular frustration even for the ground state. In this paper, we investigate analytically the critical phenomena in the model, having both randomness and frustration and we report some analytical results for it.     

Scaling in the disordered quantum antiferromagnetic chain

Numerical calculations on the disordered quantum Heisenberg antiferromagnetic chain yield low-temperature behavior independent of the detailed form of the randomness. A simple scaling interpretation, which makes contact with earlier theoretical work, of these complicated calculations is presented. An analogy with a one-parameter scaling theory of localization is explored.     

Phase transitions and critical properties in the antiferromagnetic Ising model on a layered triangular lattice with allowance for intralayer next-nearest-neighbor interactions

The phase transitions (PTs) and critical properties of the antiferromagnetic Ising model on a layered (stacked) triangular lattice have been studied by the Monte Carlo method using a replica algorithm with allowance for the next-nearest-neighbor interactions. The character of PTs is analyzed using the histogram technique and the method of Binder cumulants. It is established that the transition from the disordered to paramagnetic phase in the adopted model is a second-order PT. Static critical exponents of the heat capacity (α), susceptibility (γ), order parameter (β), and correlation radius (ν) and the Fischer exponent η are calculated using the finite-size scaling theory. It is shown that (i) the antiferromagnetic Ising model on a layered triangular lattice belongs to the XY universality class of critical behavior and (ii) allowance for the intralayer interactions of next-nearest neighbors in the adopted model leads to a change in the universality class of critical behavior.     

Phase transitions in the Ising model with transverse field

We show the existence of a phase transition in the Ising model with transverse field for dimensionsv 2 provided the transverse term is sufficiently small. This is done by proving long-range order occurs using the reflection positivity of the Hamiltonian and localization of eigenvectors.     

Extremity of the disordered phase in the Ising model on the Bethe lattice

We prove that the disordered Gibbs distribution in the ferromagnetic Ising model on the Bethe lattice is extreme forTT _c ^SG , whereT _c ^SG is the critical temperature of the spin glass model on the Bethe lattice, and it is not extreme forT _c ^SG .     

Phase diagram of an Ising model with competitive interactions on a Husimi tree and its disordered counterpart

We consider an Ising competitive model defined over a triangular Husimi tree where loops, responsible for an explicit frustration, are even allowed. We first analyze the phase diagram of the model with fixed couplings in which a “gas of noninteracting dimers (or spin liquid) — ferro or antiferromagnetic ordered state” zero temperature transition is recognized in the frustrated regions. Then we introduce the disorder for studying the spin glass version of the model: the triangular ±J model. We find out that, for any finite value of the averaged couplings, the model exhibits always a finite temperature phase transition even in the frustrated regions, where the transition turns out to be a glassy transition. The analysis of the random model is done by applying a recently proposed method which allows us to derive the critical surface of a random model through a mapping with a corresponding nonrandom model.     

Phase transformations studies on a disordered structure of lead iodide

Phase transformation studies on disordered crystals of lead iodide grown by the “gel” technique have been performed. It has been shown that the degree of disorder is reduced as a result of annealing, and that an ordered structure may appear. In some cases the disorder is completely eliminated and only the ordered structure is the product of transformation. The results have been explained in terms of the annihilation of randomly distributed stacking faults and the nucleation of new ordered stacking faults, or the migration of extended defects to a more stable configuration. Electron microscope evidence is presented in support of the above explanation.     

Phase structure of the FCC quartet Ising model

The phase structure of an Ising model with four-spin interactions defined on an FCC lattice is determined by Monte Carlo techniques. Our results show that this system undergoes a single, first order transition at the self-dual point. This resolves previous mutually contradictory conclusions which have been drawn about this model.     

Correlation functions of the Ising model of solid ortho-hydrogen in the disordered phase

In a generalized molecular field approximation the time independent correlation functions as well as the time dependent ones are calculated for the Ising model of o-H₂ in the orientationally disordered phase. In our treatment the correlations fulfill their characteristic sum rule automatically. The order parameter correlation shows the characteristic singularity at the stability limit fork=0. The time dependent correlations are calculated within the Glauber stochastic model and show critical behaviour at the stability limit.