Effective string theory on a torus: the 3d Ising domain wall

2025/10/17 by David Lima, J. M. Viana Parente Lopes, Lima, David +5
Physics and Astronomy · #Theoretical and Computational Physics #Quantum many-body systems #Physics of Superconductivity and Magnetism

paper · pdf · doi:10.48550/arxiv.2510.15206

Abstract

We use effective string theory (EST) to describe a toroidal 2d domain wall embedded in a 3d torus. In particular, we compute the free energy of the domain wall in an expansion in inverse powers of the area, up to the second non-universal order that involves the Wilson coefficient γ₃. In order to test our predictions, we simulate the 3d Ising model with anti-periodic boundary conditions, using a two-step flat-histogram Monte Carlo method in an ensemble over the boundary coupling J that delivers high-precision free energy data. The predictions from EST reproduce the lattice results with only two adjustable parameters: the string tension, 1/ℓ_s², and γ₃. We find γ₃ /|γ₃^min|= -0.82(15), which is compatible with previous estimates.

Citations

• Effective String Theory of three-dimensional SU(N) gauge theories beyond the Nambu--Gotō approximation
• Numerical tests of the large charge expansion
• Lectures on modular forms and strings
• Extremal Determinants of Laplace-Beltrami Operators for Rectangular Tori
• Monte Carlo sampling methods using Markov chains and their applications

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