平均场与短程临界动力学之间的相似性与分歧
Affinities and disagreements between Mean-field and short-range critical dynamics
摘要：
在这项工作中，我们探讨了一些有趣的细节的依赖于时间的制度的长程系统的平均场近似下的临界动力学的短程系统相比。首先，我们通过二维蒙特卡罗模拟讨论了磁化强度初始异常行为的一些机制，并与平均场模拟的结果进行了比较：自旋1/2（伊辛）和自旋1（Blume Capel模型）伊辛模型。临界点和三临界点之间的区别也进行了研究。为了进行完整的分析，我们在平均场状态下进行了短时模拟，以确定优化幂律的临界温度和不同点的临界指数，这些指数是独立计算的，即不使用文献/理论中先前的临界指数估计。我们的调查也证实了这里的分析结果。
英文摘要：
In this work, we explore some interesting details of the time-dependent regime of the long-range systems under mean-field approximation in comparison with the critical dynamics of the short-range systems. First, we discuss some mechanisms of the initial anomalous behavior of the magnetization via two-dimensional Monte Carlo simulations to later compare with results from Mean-field simulations in both: spin 1/2 (Ising) and spin 1 (Blume Capel model) Ising models. The distinction between critical and tricritical points is also investigated. For a complete analysis, we performed short-time simulations in the mean-field regime to determine the critical temperatures optimizing power laws and the critical exponents of the different points, which were independently calculated, i.e. without using previous critical exponents estimates from literature/theory. Our investigations corroborate analytical results here also developed.
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