Aspect-ratio dependence of thermodynamic Casimir forces

Alfred Hucht, Daniel Grüneberg, and Felix M. Schmidt
Phys. Rev. E 83, 051101 – Published 2 May 2011

Abstract

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 Tc. 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.

    • Received 21 December 2010

    DOI:https://doi.org/10.1103/PhysRevE.83.051101

    ©2011 American Physical Society

    Authors & Affiliations

    Alfred Hucht, Daniel Grüneberg, and Felix M. Schmidt

    • Fakultät für Physik, Universität Duisburg–Essen, D-47048 Duisburg, Germany

    Article Text (Subscription Required)

    Click to Expand

    References (Subscription Required)

    Click to Expand
    Issue

    Vol. 83, Iss. 5 — May 2011

    Reuse & Permissions
    Access Options
    Author publication services for translation and copyediting assistance advertisement

    Authorization Required


    ×
    ×

    Images

    ×

    Sign up to receive regular email alerts from Physical Review E

    Log In

    Cancel
    ×

    Search


    Article Lookup

    Paste a citation or DOI

    Enter a citation
    ×