High precision Monte Carlo simulations of interfaces in the three-dimensional Ising model: a comparison with the Nambu-Goto effective string model

TL;DR

The paper tests the Nambu-Goto effective string description for interfaces in the 3D Ising model by performing high-precision Monte Carlo simulations of the interface free energy with periodic boundary conditions. By enforcing an interface via an antiferromagnetic seam and measuring $F_s$, the authors compare results to the NLO predictions of the Nambu-Goto model, finding good agreement for $\sqrt{\sigma}\,L \gtrsim 2$ (equivalently $L \gtrsim 2.5N_t$) in the coupling regimes near the phase transition. They show that deviations at smaller $\sqrt{\sigma}\,L$ can be attributed to higher-order corrections, while asymmetries in cross-sections reveal significant beyond-NLO contributions. The work strengthens the case for effective-string descriptions in confinement-related observables and highlights the interface as a pristine setting to refine these models and understand boundary effects in related lattice gauge theories.

Abstract

Motivated by the recent progress in the effective string description of the interquark potential in lattice gauge theory, we study interfaces with periodic boundary conditions in the three-dimensional Ising model. Our Monte Carlo results for the associated free energy are compared with the next-to-leading order (NLO) approximation of the Nambu-Goto string model. We find clear evidence for the validity of the effective string model at the level of the NLO truncation.

Figures (1)

• Figure 1: $F_s - \sigma L^2 + 0.5 \ln \sigma$ as function of $\sqrt{\sigma} L$ for $\beta_{\hbox{\tiny{s}}}=0.226102$, $0.236025$ and $0.27604$. In all cases $L_1=L_2=L$ and $L_0 = 3 L$. The values for $\sigma$ are taken from table \ref{['basictab']}. We have checked that the plot does not change significantly, when $\sigma$ is varied within the quoted errorbars. The dotted lines should only guide the eye.