Violation of finite-size scaling for the free energy near criticality

2001/12/17 by X. S. Chen, Chen, X. S., V. Dohm +1
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Quantum Electrodynamics and Casimir Effect #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.48550/arxiv.cond-mat/0112310

4 pages, no figure

arxiv created 2001/12/17 · openalex publication_date 2001/12/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The singular part of the finite-size free energy density f_s of the O(n) symmetric ϕ⁴ field theory is calculated for confined geometries of linear size L with periodic boundary conditions in the large-N limit and with Dirichlet boundary conditions in one-loop order. We find that both a sharp cutoff and a subleading long-range interaction cause a non-universal L dependence of f_s near T_c. For film geometry this implies a non-universal critical Casimir force with an algebraic L dependence that dominates the exponential finite-size scaling behavior above T_c for both periodic and Dirichlet boundary conditions.

Related

• Thermodynamic Casimir Effect in the large-n limit
• Finite-Size and Finite-Temperature Effects in the Conformally Invariant O(N) Vector Model for 2
• Universal finite-size scaling in high-dimensional critical phenomena
• Boundary conditions and the critical Casimir force on an Ising model film: exact results in one and two dimensions
• Boundary conditions and universal finite-size scaling for the hierarchical |φ|⁴ model in dimensions 4 and higher