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

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 ${\hat{I}}_3^3$. 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, $1/{\ell }_s^2$, and ${\hat{I}}_3^3$. We find $γ_3 /|γ_3^{\text{min}}|= -0.82(15)$, which is compatible with previous estimates.

22 pages, 13 figures