Aspect-ratio dependence of thermodynamic Casimir forces.
Aspect-ratio dependence of thermodynamic Casimir forces.
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热力学卡西米尔力的纵横比依赖性。
DOI：
10.1103/physreve.83.051101
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
Felix M. Schmidt
中科院分区：
文献类型：
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作者：
A. Hucht;Daniel Grüneberg;Felix M. Schmidt
我们考虑L（⊥）×L（∥）×L（∥）长方体几何中的三维Ising模型，它具有有限的纵横比ρ=L(⊥)/L（∥）和沿所有方向的周期性边界条件。对于该模型，采用蒙特卡罗模拟的方法对多余自由能和热力学卡西米尔力的有限尺度函数进行了数值计算。蒙特卡罗结果与最近在高于和略低于体临界温度T(c)的温度下的伊辛普适类的场理论结果比较好。此外，精确地计算了任意ρ下二维Ising模型的多余自由能和卡西米尔力标度函数，并与三维情况进行了比较。我们给出了一个一般的论点，卡西米尔力在ρ=1的临界点处消失，在ρ>1的周期系统中变为排斥性。
We consider the three-dimensional Ising model in a L(⊥)×L(∥)×L(∥) cuboid geometry with a finite aspect ratio ρ=L(⊥)/L(∥) and periodic boundary conditions along all directions. For this model the finite-size scaling functions of the excess free energy and thermodynamic Casimir force are evaluated numerically by means of Monte Carlo simulations. The Monte Carlo results compare well with recent field theoretical results for the Ising universality class at temperatures above and slightly below the bulk critical temperature T(c). Furthermore, the excess free energy and Casimir force scaling functions of the two-dimensional Ising model are calculated exactly for arbitrary ρ and compared to the three-dimensional case. We give a general argument that the Casimir force vanishes at the critical point for ρ=1 and becomes repulsive in periodic systems for ρ>1.