Gaussian random field p-spin-interaction ising model in a transverse field

The Gaussian random field Ising model with p-spin interactions in the presence of a transverse field is studied by combining the Suzuki-Trotter approach and the thermodynamic perturbation theory. The first-order phase transitions are found in the limit p → ∞, in contrast to the cases with p=2.     

On the susceptibility of the one-dimensional Ising chain

The elements of the tensor of the susceptibility and the staggered susceptibility of a one-dimensional I Ising chain, with xx couplings between the spins are investigated in the presence of a magnetic field b parallel with or perpendicular to the x direction. Exact expressions are given for all susceptibilities, apart from the parallel susceptibilities in a transverse field which are evaluated by perturbation calculation. Special attention is paid to the conditions under which a susceptibility can have a minimum for b = 0. Furthermore, a system with weakly coupled Ising chains is considered on the basis of a model hamiltonian with separable interchain interactions.     

Thermodynamics of the quantum and classical Ising models with skew magnetic field

The thermodynamics of the unitary (normalized spin) quantum and classical Ising models with skew magnetic field, for |J|β?0.9, is derived for the ferromagnetic and antiferromagnetic cases. The high-temperature expansion (β-expansion) of the Helmholtz free energy is calculated up to order β⁷ for the quantum version (spin S≥1/2) and up to order β¹⁹ for the classical version. In contrast to the S=1/2 case, the thermodynamics of the transverse Ising and that of the XY model for S>1/2 are not equivalent. Moreover, the critical line of the T=0 classical antiferromagnetic Ising model with skew magnetic field is absent from this classical model, at least in the temperature range of |J|β?0.9.     

Spin and energy coupling in the Ising model with a transverse field: One dimension,T=∞

The dynamics of the one dimensional Ising model with a transverse field is studied in the limit T = ∞. Numerical studies of the classical chain and exact calculations for the spin $\text{1}\text{2}$ chain indicate the presence of an energy density term in the dynamic spin susceptibility along the direction of the field.     

The quantum transverse spin-2 Ising model with a bimodal random-field in the pair approximation

In this paper, we have investigated the bimodal random-field spin-2 Ising system in a transverse field by combining the pair approximation with the discretized path-integral representation. The exact equations for the second-order phase transition lines and tricritical points are obtained in terms of the random field H, the transverse field G and the coordination number z. It is found that there are some critical values for H and G where the tricritical points disappear for given z. We have also observed that the system presents reentrant behavior which may be caused by the quantum effects and randomness. The phase diagram with respect to the random field and the second-order phase transition temperature are studied extensively for given values of the transverse field and the coordination number.     

Critical properties of a random transverse crystal field Ising model with bond dilution

Within effective field theory (EFT), the critical properties of a random transverse crystal field Ising model with bond dilution are studied on a square lattice. Under both weak and strong bond dilution conditions, we consider three cases (α = 0,±0.5) of a transverse crystal field ratio, obtaining global phase diagrams in T−D _x space for changes in the random transverse crystal field concentration. The phase diagrams obtained for a weak bond dilution are very similar in shape to those of pure bond but with decreases in corresponding ordered phases and critical values. However, the phase diagrams for a strong bond dilution exhibit varieties, including a change in reentrant phenomenon, the occurrence of transverse crystal field degeneration, and the opposite direction crossover of temperature peak value.     

Symmetric vertex models on planar random graphs

We solve a 4-(bond)-vertex model on an ensemble of 3-regular (Φ³) planar random graphs, which has the effect of coupling the vertex model to 2D quantum gravity. The method of solution, by mapping onto an Ising model in field, is inspired by the solution by Wu et.al. of the regular lattice equivalent – a symmetric 8-vertex model on the honeycomb lattice, and also applies to higher valency bond vertex models on random graphs when the vertex weights depend only on bond numbers and not cyclic ordering (the so-called symmetric vertex models).The relations between the vertex weights and Ising model parameters in the 4-vertex model on Φ³ graphs turn out to be identical to those of the honeycomb lattice model, as is the form of the equation of the Ising critical locus for the vertex weights. A symmetry of the partition function under transformations of the vertex weights, which is fundamental to the solution in both cases, can be understood in the random graph case as a change of integration variable in the matrix integral used to define the model.Finally, we note that vertex models, such as that discussed in this paper, may have a role to play in the discretisation of Lorentzian metric quantum gravity in two dimensions.     

Quantum Phase Transitions in <Emphasis Type="Italic">s</Emphasis> = 1/2 Ising Chain in a Regularly Alternating Transverse Field

We consider the ground-state properties of the s = 1/2 Ising chain in a transverse field which varies regularly along the chain having a period of alternation 2. Such a model, similarly to its uniform counterpart, exhibits quantum phase transitions. However, the number and the position of the quantum phase transition points depend on the strength of transverse field modulation. The behaviour in the vicinity of the critical field in most cases remains the same as for the uniform chain (i.e. belongs to the square-lattice Ising model universality class). However, a new critical behaviour may also arise. We report the results for critical exponents obtained partially analytically and partially numerically for very long chains consisting of a few thousand sites.     

Autocorrelation function of the x-component of the magnetization in the one-dimensional XY-model

Exact expressions are derived for the time-dependent correlation functions of the x and y component of the magnetization for the one-dimensional anisotropic XY-model ($\text{S=}\text{1}\text{2}$) in zero field in the high-temperature limit. As a corollary, the correlation functions for the Ising chain in a transverse field are obtained.     

Spin dynamics in hole-doped two-dimensional S = 1/2 Heisenberg antiferromagnets: 63Cu NQR relaxation in La2-xSrxCuO4 for x ≤ 0.04

A cluster algorithm formulated in continuous (imaginary) time is presented for Ising models in a transverse field. It works directly with an infinite number of time-slices in the imaginary time direction, avoiding the necessity to take this limit explicitly. The algorithm is tested at the zero-temperature critical point of the pure two-dimensional (2d) transverse Ising model. Then it is applied to the 2d Ising ferromagnet with random bonds and transverse fields, for which the phase diagram is determined. Finite size scaling at the quantum critical point as well as the study of the quantum Griffiths-McCoy phase indicate that the dynamical critical exponent is infinite as in 1d. Received 6 November 1998     

Absence of Replica Symmetry Breaking in the Transverse and Longitudinal Random Field Ising Model

It is proved that replica symmetry is not broken in the transverse and longitudinal random field Ising model. In this model, the variance of spin overlap of any component vanishes in any dimension almost everywhere in the coupling constant space in the infinite volume limit. The weak Fortuin–Kasteleyn–Ginibre property in this model and the Ghirlanda–Guerra identities in artificial models in a path integral representation based on the Lie–Trotter–Suzuki formula enable us to extend Chatterjee’s proof for the random field Ising model to the quantum model.     

Density-matrix spectra for integrable models

The spectra which occur in numerical density-matrix renormalization group (DMRG) calculations for quantum chains can be obtained analytically for integrable models via corner transfer matrices. This is shown in detail for the transverse Ising chain and the uniaxial XXZ Heisenberg model and explains in particular their exponential character in these cases.     

横场中非束缚类准周期伊辛链的赝临界点

本文系统地研究了有限尺寸下非束缚类准周期量子伊辛链在横场中的赝临界点的行为. 首先, 通过计算平均磁矩和协作参量, 发现这两个量的导数随着横场的变化都会出现两个清晰的峰. 这与束缚类伊辛链和无序伊辛链的结果明显不同. 其次, 研究了横场中赝临界点的概率分布情况, 发现概率分布并不是高斯型的. 这也与无序的结果不同. 最后, 分析了赝临界点产生的原因, 发现赝临界点是由非束缚类准周期伊辛链中的集团结构造成的.     

Thermodynamical properties of the transverse Ising model

A new effective field theory is proposed and used to derive the thermodynamical properties of the transverse Ising model. The formalism is based on an exact formal spin identity for the two-state transverse Ising model and utilizes an exponential operator technique. The method, which can explicitly and systematically include correlation effects, is illustrated in several lattice structures by employing its simplest approximation version (in which spin-spin correlations are neglected). The lines of critical points in the Ω-T plane as well as the thermal behaviour of both transverse and longitudinal magnetizations are analysed for square and simple cubic lattices. It is shown that the present formalism, in spite of its simplicity, yields results which represent a remarkable improvement on the standard mean field treatment (MFA).     

New Results for the Correlation Functions of the Ising Model and the Transverse Ising Chain

In this paper we show how an infinite system of coupled Toda-type nonlinear differential equations derived by one of us can be used efficiently to calculate the time-dependent pair-correlations in the Ising chain in a transverse field. The results are seen to match extremely well long large-time asymptotic expansions newly derived here. For our initial conditions we use new long asymptotic expansions for the equal-time pair correlation functions of the transverse Ising chain, extending an old result of T.T. Wu for the 2d Ising model. Using this one can also study the equal-time wavevector-dependent correlation function of the quantum chain, a.k.a. the q-dependent diagonal susceptibility in the 2d Ising model, in great detail with very little computational effort. Supported in part by the National Science Foundation under grant PHY 07-58139 and by the Australian Research Council under Project ID: LX0989627.     

On the random binary Ising system with a transverse field

The transition temperature and paramagnetic susceptibility in the random binary Ising model with a transverse field are obtained. The system is composed of ferro- and antiferromagnetic spins. It is found that ferro- and antiferromagnetic states coexist in some cases.     

Effect of the transverse field on the site-diluted Ising model in a longitudinal random field

Phase diagrams and magnetization curves of a diluted spin-3/2 transverse Ising model in a random field on honeycomb lattices are investigated by the use of an effective-field theory with correlations. The tricritical point is found in the system, in contrast to the corresponding spin-1/2 Ising counterpart. The possible reentrant phenomena displayed by the system due to the competition effects that occur for appropriate ranges of the random and transverse fields are investigated.     

The classical Ising model: A quantum renormalization group approach

Proceeding from the equivalence between the d-dimentional classical Ising model and the (d?1)-dimentional quantum mechanical Ising model in a transverse magnetic field, we study the critical properties of the classical model via the quantum mechanical model. Quantum renormalization group transformations based on the truncation method and the ground state projection operator method are used to calculate the critical exponents. They are found to agree well with the “exact” values.     

Variational principle for regular and random Ising models on the cactus tree or on the usual lattice in the “cactus approximation”

The distribution functions and the free energy are expressed in terms of the effective fields for the regular and random Ising models of an arbitrary spin S on the generalized cactus tree. The same expressions apply to systems on the usual lattice in the “cactus approximation” in the cluster variation method. For an ensemble of random Ising models of an arbitrary spin S on the generalized cactus tree, the equation for the probability distribution function of the effective fields is set up and the averaged free energy is expressed in terms of the probability distribution. The same expressions apply to the system on the usual lattice in the “cactus approximation”. We discuss the quantities on the usual lattice when the system or the ensemble of random systems has the translational symmetry. Variational properties of the free energy for a system and of the averaged free energy for an ensemble of random systems are noted. The “cactus approximations” are applicable to the Heisenberg model as well as to the Ising model of an arbitrary spin, and to ensembles of random systems of these models.