在蜂格子上的丧的J1的分区函数零-J2的Ising模型
Denis Gessert1,2, Martin Weigel3, Wolfhard Janke1
1Institut für Theoretische Physik, Leipzig University, IPF 231101, 04081 Leipzig, Germany.
通过分析丧的Ising模型,这项研究揭示了分区函数零 (Fisher和Lee-Yang) 为理解关键行为提供了强大的方法,特别是当传统的有限大小缩放因丧效应而复杂时.
科学领域:
- 统计力学 统计力学
- 凝聚物质物理学 凝聚物质物理学
- 计算物理 计算物理
背景情况:
- 在蜂巢网格上研究具有竞争相互作用 (J1>0,J2<0) 的挫败的Ising模型.
- 了解挫折对关键现象和阶段过渡的影响.
- 探索传统的有限尺寸缩放 (FSS) 方法的局限性,原因是对缩放的纠正.
研究的目的:
- 为了分析费舍尔和李零的有限尺寸缩放,在一个丧的Ising模型中.
- 为了比较分区函数零分析与传统FSS方法的有效性.
- 为了确定Ising通用性类对挫败系统的适用性.
主要方法:
- 使用累积方法计算费舍尔和李的零.
- 根据磁化和磁性易感性,与传统的FSS进行比较.
- 将缩放行为作为交互比率R=J2/J1.1的函数的分析.
主要成果:
- 分区函数零分析和传统的FSS在挫败下表现出不同的行为.
- 为了实际实施,研究了累积方法的收性.
- 证实了Ising通用性类的下降到R=-0.22,其中传统的FSS不那么有说服力.
结论:
- 对分区函数零的分析是传统的FSS对挫败模型的有价值补充.
- 这种方法有效地映射相位图在存在强大的校正缩放.
- 提供了一个更可靠的工具来确定复杂磁系统中的通用性类.
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