Gallardo R A, Idigoras O, Landeros P, Berger A
Departamento de Física, Universidad Técnica Federico Santa María, Avenida España 1680, Valparaíso, Chile.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Nov;86(5 Pt 1):051101. doi: 10.1103/PhysRevE.86.051101. Epub 2012 Nov 2.
We have analyzed the dynamic phase transition of the kinetic Ising model in mean-field approximation by means of an analytical approach. Specifically, we study the evolution of the system under the simultaneous influence of time-dependent and time-independent magnetic fields. We demonstrate that within the approximate analytical treatment of our approach, the dynamic phase transition exhibits power-law dependencies for the order parameter that have the same critical exponents as the mean-field equilibrium case. Moreover we have obtained an equation of state, with which we can prove that the time-independent field component is effectively the conjugate field of the order parameter. Our analysis is limited to the parameter range, in which only second-order phase transitions occur, i.e., for small applied field amplitudes and temperatures close to the Curie point. In order to ensure the reliability of our analytical results we have corroborated them by comparison to numerical evaluations of the same model.
我们通过一种解析方法，在平均场近似下分析了动力学伊辛模型的动态相变。具体而言，我们研究了在随时间变化和不随时间变化的磁场同时影响下系统的演化。我们证明，在我们方法的近似解析处理中，动态相变对于序参量呈现幂律依赖关系，其临界指数与平均场平衡情况相同。此外，我们得到了一个状态方程，利用它可以证明不随时间变化的场分量实际上是序参量的共轭场。我们的分析限于仅发生二阶相变的参数范围，即对于小的外加场振幅以及接近居里点的温度。为了确保我们解析结果的可靠性，我们通过与同一模型的数值评估结果进行比较来加以证实。
