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Communications in Theoretical Physics

Magnetic Properties of Transverse Ising Model under a Time Oscillating Longitudinal Field

Xiaoling Shi, Li Wang, Guozhu Wei

Published Apr 1, 2011• 14 citations
Publisher

Abstract

A transverse Ising spin system, in the presence of time-dependent longitudinal field, is studied by the effective-field theory (EFT). The effective-field equations of motion of the average magnetization are given for the simple cubic lattice (Z = 6) and the honeycomb lattice (Z = 3). The Liapunov exponent λ is calculated for discussing the stability of the magnetization and it is used to determine the phase boundary. The dynamic phase transition diagrams in h 0 /ZJ — Γ/ZJ plane and in h 0 /ZJ — T/ZJ plane have been drawn, and there is no dynamical tricritical point on the dynamic phase transition boundary. The effect of the thermal fluctuations upon the dynamic phase boundary has been discussed.

DOI
10.1088/0253-6102/55/4/37

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A transverse Ising spin system, in the presence of time-dependent longitudinal field, is studied by the effective-field theory (EFT). The effective-field equations of motion of the average magnetization are given for the simple cubic lattice (Z = 6) and the honeycomb lattice (Z = 3). The Liapunov exponent λ is calculated for discussing the stability of the magnetization and it is used to determine the phase boundary. The dynamic phase transition diagrams in h 0 /ZJ — Γ/ZJ plane and in h 0 /ZJ — T/ZJ plane have been drawn, and there is no dynamical tricritical point on the dynamic phase transition boundary. The effect of the thermal fluctuations upon the dynamic phase boundary has been discussed.
As an analytical method, the effective-field theory (EFT) is used to study the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field. The effective-field equations of motion of the average magnetization are given for the honeycomb lattice (Z = 3). The Liapunov exponent λ is calculated for discussing the stability of the magnetization and it is used to determine the phase boundary. In the field amplitude h 0 /ZJ-temperature T/ZJ plane, the phase boundary separating the dynamic ordered and the disordered phase has been drawn. In contrast to previous analytical results that predicted a tricritical point separating a dynamic phase boundary line of continuous and discontinuous transitions, we find that the transition is always continuous. There is inconsistency between our results and previous analytical results, because they do not introduce sufficiently strong fluctuations.
一个横向的 Ising 旋转系统，面对时间依赖者纵的地，被有效地的理论(水蜥) 学习。平均磁化的运动的有效地的方程为简单立方的格子被给(Z = 6 ) 并且蜂房格子(Z = 3 ) 。Liapunov 代表为讨论磁化的稳定性被计算，决定阶段边界被用来。在 h0/ZJ /ZJ 飞机并且在 h0/ZJ T/ZJ 飞机的动态阶段转变图被拉了，并且动态阶段转变边界上没有动态 tricritical 点。在动态阶段边界之上的热变化的效果被讨论了。
Abstract Within the framework of the effective‐field theory with correlations, a spin‐$ {3 \over 2} $ transverse Ising model in the longitudinal random‐field on a honeycomb lattice is studied. The phase diagrams and the behavior of the tricritical point are examined. The possible re‐entrance phenomena displayed by the system due to the competition effects that occur for the appropriate ranges of the random and transverse field are investigated. The longitudinal and transverse magnetizations, the longitudinal quadrupolar moments and internal energy are given numerically for a honeycomb lattice (z = 3). (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The transverse spin-2 Ising ferromagnetic model with a longitudinal crystal-field is studied within the mean-field theory based on Bogoliubov inequality for the Gibbs free energy. The ground-state phase diagram and the tricritical point are obtained in the transverse field Ω/zJ-longitudinal crystal D/zJ field plane. We find that there are the first order-order phase transitions in a very small range of D/zJ besides the usual first order-disorder phase transitions and the second order-disorder phase transitions.