The interface free energy: comparison of accurate Monte Carlo results for the 3D Ising model with effective interface models

2007/07/31 by Michele Caselle, Martin Hasenbusch, Marco Panero · 2 citations
Mathematics · Physics and Astronomy · #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.soft #hep-lat #hep-th

paper · pdf · doi:10.1088/1126-6708/2007/09/117

published as JHEP0709:117,2007 · 44 pages, 7 figures; v2: clarified some aspects discussed in section 2, added references, corrected typos, version published in JHEP

openalex publication_date 2007/09/26 · arxiv created 2007/09/27 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We provide accurate Monte Carlo results for the free energy of interfaces with periodic boundary conditions in the 3D Ising model. We study a large range of inverse temperatures, allowing to control corrections to scaling. In addition to square interfaces, we study rectangular interfaces for a large range of aspect ratios u=L₁/L₂. Our numerical results are compared with predictions of effective interface models. This comparison verifies clearly the effective Nambu-Goto model up to two-loop order. Our data also allow us to obtain the estimates T_c sigma^-1/2=1.235(2), m₀++ sigma^-1/2=3.037(16) and R₊=f₊² sigma₀ =0.387(2), which are more precise than previous ones.

Citations

• Static potential, force, and flux-tube profile in 4D compact U(1) lattice gauge theory with the multi-level algorithm
• A Monte Carlo study of leading order scaling corrections of phi⁴ theory on a three dimensional lattice

Cited by

• Symmetries and exponential error reduction in Yang–Mills theories on the lattice
• Phase transition properties of 3D Potts models