论文标题
通过近似其功能积分来限制每个粒子的自由能
Limiting free energy per particle for Ising Model by approximating its functional integral
论文作者
论文摘要
在没有外部磁场的情况下，有许多方法旨在研究3维（3D）ISING模型的每个粒子（LFEPP）的极限自由能。这些方法很优雅，但大多数方法很复杂，通常需要专业知识和特殊技能。在这里，我们使用经典的数学物理方法从其功能积分中近似其功能积分的LFEPP。 1维（1D）至3D ISING模型的结果LFEPP具有相似的结构和形式。然后，我们验证这些LFEPP对于1D和2维（2D）模型的两个限制案例以及2D模型的关键反度$ Z_C $正确。基于这些验证，我们自然地得出了LFEPP和3D模型的$ z_c $（$ \ of约0.21 \ sim 0.22 $）。此外，我们建议使用具有外部磁场的1D-3D ISING模型的类似LFEPP，尽管它们太复杂了。
There have been a lot of methods aimed at studying the limiting free energy per particle (LFEPP) for 3-dimensional (3D) Ising model in absence of an external magnetic field. These methods are elegant, but most of them are complicated and often require specialized knowledge and special skills. Here we approximate the LFEPP for Ising model from its functional integral using classic mathematical-physical methods. The resulting LFEPPs for 1-dimensional (1D) to 3D Ising model have similar structures and forms. We then verify that these LFEPPs are correct for two limiting cases of the 1D and 2-dimensional (2D) models, as well as for the critical inverse temperature $z_c$ of the 2D model. Based on these verifications, we derive naturally the LFEPP and the $z_c$ ($\approx 0.21\sim 0.22$) for the 3D model. Furthermore, we suggest similar LFEPPs for 1D-3D Ising models with an external magnetic field, although they are too complicated.
