A new approximation for the dynamics of the transverse ising model

An improved mean field theory, the Reaction Field Approximation, which was previously used to obtain the static properties of model systems of localized spins (Heisenberg, XY, Ising and also more complicated interaction Hamiltonians) is extendend so that dynamical properties of the Ising model in presence of a transverse field can also be calculated. Theq- and ω-dependent susceptibility is obtained as function of field and temperature, from which the dynamic correlation functions can also be obtained. The dependence of the critical temperature on the transverse field is calculated and a phase diagram is presented.     

The critical properties of magnetic films

Within the framework of the transverse Ising model and by using the effective field theory with a probability distribution technique that accounts for the self spin correlations, we have studied the critical properties of an L-layer film of simple cubic symmetry in which the exchanges strength are assumed to be different from the bulk values in N_S surface layers. We derive and illustrate the expressions for the phase diagrams, order parameter profiles and susceptibility. In such films, the critical temperature can shift to either lower or higher temperature compared with the corresponding bulk value. We calculate also some magnetic properties of the film, such as the layer magnetizations, their averages and their profiles and the longitudinal susceptibility of the film. The film longitudinal susceptibility still diverges at the film critical temperature as does the bulk longitudinal susceptibility.     

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.     

Corner transfer matrices of the triangular Ising model

Recently, a new technique for investigating the zero-field, eight-vertex model on the square lattice using corner transfer matrices was suggested by Baxter. In this paper these ideas are applied to the anisotropic, ferromagnetic, triangular Ising lattice in zero field below its critical temperature. The diagonal form of the corner transfer matrix for the triangular lattice shows essentially the same structure as that for the square Ising lattice. The spontaneous magnetization can be obtained easily and agrees with that previously derived.     

The sequence of structural phase transitions in systems with a four-well potential

The theory of order-disorder phase transitions is discussed for systems with a four-well potential. It is shown that the model can be generalized to the case of the well-known Ising model in a transverse field. It is also shown that two or three crystalline phases can emerge as the temperature is reduced. Fiz. Tverd. Tela (St. Petersburg) 39, 2217–2219 (December 1997)     

Higher-order susceptibilities of the regular and the random Ising model on the Cayley tree. I

Explicit expressions for the fourth-order susceptibility (⁴), the fourth derivative of thebulk free energy with respect to the external field, are given for the regular and the random-bond Ising model on the Cayley tree in the thermodynamic limit, at zero external field. The fourth-order susceptibility for the regular system diverges at temperature T _c ⁽⁴⁾ = 2k _B ^–1 J/ln{1+2/[(z–1)^3/4–1]}, confirming a result obtained by Müller-Hartmann and Zittartz [Phys. Rev. Lett. 33:893 (1974)]; Herez is the coordination number of the lattice,J is the exchange integral, andk _B is the Boltzmann constant. The temperatures at which ⁽⁴⁾ and the ordinary susceptibility (²) diverge are given also for the random-bond and the random-site Ising model and for diluted Ising models.     

Antiferromagnetic model and magnetization plateaus on the zigzag ladder with two- and three-site exchanges

The Ising approximation is proposed for the Heisenberg model with two- and three-spin exchange interactions on a zigzag ladder placed in a strong magnetic field. Using the transfer matrix technique the magnetization is calculated and compared with the results obtained in the dynamical recursive approach. Magnetization plateaus are found at m=0 and with the two- and three-spin exchanges. The magnetic susceptibility in small and large zigzag ladders for various exchange parameters and temperatures is also analyzed. As temperature decreases the magnetic susceptibility versus magnetic field shows the formation of spin pseudogaps and transformation from double to four peak structure. Small clusters also exhibit characteristic features of large thermodynamic systems.     

The compensation temperature study of the mixed Ising ferrimagnetic spin system with crystal field in a transverse field

Abstract. The magnetic properties of the nearest-neighbor interaction mixed spin-1/2 and spin-1 Ising ferrimagnetic spin system with crystal field in a transverse field are investigated within the framework of the effective-field theory. Particular emphasis is given to the honeycomb lattice with coordination number Z = 3 for which magnetizations are obtained. If transverse field Ω varies in the certain ranges, we find that the compensation temperature is obtained for the value of the crystal field D in a restricted region. We discuss in detail the influence of the transverse field on the behaviors of the compensation point and magnetization curves in this paper.     

An introduced effective-field theory study of spin-1 transverse Ising model with crystal field anisotropy in a longitudinal magnetic field

A spin-1 transverse Ising model with longitudinal crystal field in a longitudinal magnetic field is examined by introducing an effective field approximation (IEFT) which includes the correlations between different spins that emerge when expanding the identities. The effects of the crystal field as well as the transverse and longitudinal magnetic fields on the thermal and magnetic properties of the spin system are discussed in detail. The order parameters, Helmholtz free energy, entropy and specific heat curves are calculated numerically as functions of the temperature and Hamiltonian parameters. A number of interesting phenomena such as reentrant phenomena originating from the temperature, crystal field, transverse and longitudinal magnetic fields have been found.     

Existence of phase transitions for quantum lattice systems

We prove that the following lattice systems:

1. anisotropic Heisenberg model,
2. Ising model with transverse magnetic field,
3. quantum lattice gas with hard cores extending over nearest neighbours,

exhibit phase transitions if the temperature is sufficiently low and the transverse (or kinetic) part of the interaction sufficiently small.     

Rigidity of Interfaces in the Falicov–Kimball Model

We analyze the thermodynamic properties of interfaces in the three-dimensional Falicov–Kimball model, which can be viewed as a primitive quantum lattice model of crystalline matter. In the strong coupling limit, the ionic subsystem of this model is governed by the Hamiltonian of an effective classical spin model whose leading part is the Ising Hamiltonian. We prove that the 100 interface in this model, at half-filling, is rigid, as in the three-dimensional Ising model. However, despite the above similarities with the Ising model, the thermodynamic properties of its 111 interface are very different. We prove that even though this interface is expected to be unstable for the Ising model, it is stable for the Falicov–Kimball model at sufficiently low temperatures. This rigidity results from a phenomenon of ground-state selection and is a consequence of the Fermi statistics of the electrons in the model.     

Gap-behavior in the vicinity of a saturation transverse field

We have studied the behavior of the energy gap of the 1D AF spin- XXZ model in a transverse magnetic field (h) using the exact diagonalization technique. The ground state phase diagram consists of two spin-flop and paramagnetic phases. Using a modified finite-size scaling approach, we have computed the critical exponent of the energy gap in the vicinity of the critical transverse field h_c(Δ). Our numerical results confirm that the continuous phase transition from the spin-flop phase to the paramagnetic one is in the universality class of the Ising model in the transverse field (ITF). By applying conformal estimates of a small perturbation (h≪1), we have also justified our numerical results.     

Weak Singularities of the Isothermal Entropy Change as the Smoking Gun Evidence of Phase Transitions of Mixed-Spin Ising Model on a Decorated Square Lattice in Transverse Field

The magnetocaloric response of the mixed spin-1/2 and spin-S (S>1/2) Ising model on a decorated square lattice is thoroughly examined in presence of the transverse magnetic field within the generalized decoration-iteration transformation, which provides an exact mapping relation with an effective spin-1/2 Ising model on a square lattice in a zero magnetic field. Temperature dependencies of the entropy and isothermal entropy change exhibit an outstanding singular behavior in a close neighborhood of temperature-driven continuous phase transitions, which can be additionally tuned by the applied transverse magnetic field. While temperature variations of the entropy display in proximity of the critical temperature Tc a striking energy-type singularity (T−Tc)log|T−Tc|, two analogous weak singularities can be encountered in the temperature dependence of the isothermal entropy change. The basic magnetocaloric measurement of the isothermal entropy change may accordingly afford the smoking gun evidence of continuous phase transitions. It is shown that the investigated model predominantly displays the conventional magnetocaloric effect with exception of a small range of moderate temperatures, which contrarily promotes the inverse magnetocaloric effect. It turns out that the temperature range inherent to the inverse magnetocaloric effect is gradually suppressed upon increasing of the spin magnitude S.     

Exact results for the dynamics of one-dimensional spin-systems

In this contribution we discuss the spin-dynamics of anisotropic one-dimensional spin 1/2X-Y-chains in a magnetic field. For special values of the parameters we solve the equation of motion for several spin-operators exactly. These results we use to calculate longitudinal and transverse dynamical correlation functions at temperatureT=, for an Ising chain in a transverse field also the first-order high-temperature correction is given.     

Thermodynamic properties of the mixed spin-1/2 and spin-1 Ising chain with both longitudinal and transverse single-ion anisotropies

The mixed spin-1/2 and spin-1 Ising chain with both longitudinal and transverse single-ion anisotropies is solved exactly by means of a mapping to the spin-1/2 Ising chains with alternating transverse fields and the Jordan-Wigner transformation. Within this scheme, the thermodynamic quantities of this model are rigorously determined by a recursion formula derived for the partition function based on the reduced spin-1/2 transverse Ising model. The corresponding thermodynamic properties are calculated and discussed.     

Solution of the long-range gaussian-random Ising model

The spin glass model of Edwards and Anderson is solved for Ising spins starting from a renormalized diagrammatic expansion. One gets two qualitatively distinct phases for arbitrary external field. The high temperature phase is identical with the solution of Sherrington and Kirkpatrick. The low temperature phase does not have unphysical properties forT0, in contrast to previous investigations.     

One-way quantum deficit and quantum coherence in the anisotropic <Emphasis Type="Italic">XY</Emphasis> chain

In this study, we investigate pairwise non-classical correlations measured using a one-way quantum deficit as well as quantum coherence in the XY spin-1/2 chain in a transverse magnetic field for both zero and finite temperatures. The analytical and numerical results of our investigations are presented. In the case when the temperature is zero, it is shown that the one-way quantum deficit can characterize quantum phase transitions as well as quantum coherence. We find that these measures have a clear critical point at λ = 1. When λ ≤ 1, the one-way quantum deficit has an analytical expression that coincides with the relative entropy of coherence. We also study an XX model and an Ising chain at the finite temperatures.     

Ground-state magnetic properties of the spin-2 transverse Ising model

The ground-state magnetic properties of the spin-2 transverse Ising model with a longitudinal crystal field are studied within the framework of mean-field theory (MFT) and effective-field theory (EFT), respectively. The phase diagrams and magnetization curves are examined in detail. It is found that the system exhibits a tricritical behavior in the ground-state phase diagrams. Some interesting phenomena have been found, especially the first-order phase transition from one ordered phase to the other ordered phase, which is due to the high spin. The spin correlation has important effect on the magnetic properties of the system. We also find that the ground-state phase diagrams of the spin-2 transverse Ising model are very different from those of the spin-3/2 transverse Ising model.     

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).     

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.