Effective strings and particles interacting in 3D: the Ising model

TL;DR

This paper investigates how a fluctuating domain wall in three dimensions influences bulk properties in the 3D Ising model, deriving an effective interaction and testing universal predictions through Monte Carlo simulations.

Contribution

It introduces an effective interaction framework between domain walls and bulk modes, identifying regimes where universal behavior emerges and validating predictions with simulations.

Findings

Universal corrections to wall free energy are controlled by a renormalized coupling.

Large-distance two-point functions exhibit Gaussian broadening consistent with wall fluctuations.

Monte Carlo simulations confirm the predicted rough-wall broadening behavior.

Abstract

We study how a fluctuating domain wall in three dimensions modifies bulk observables in a gapped phase. We introduce an effective interaction between the wall and the lightest bulk massive mode, and identify the regime in which this description is controlled: nearly on-shell bulk exchange with small momentum along the wall. In this regime, several observables are controlled by a renormalized dimensionless coupling $\lambda$, including the large-$L_z$ correction to the wall free energy and the large-$|x_\perp|$ tail of two-point functions in the presence of the wall. Other observables, such as one-point functions and two-point functions in the nearby-regime, retain non-universal dependence on operator data and on the bulk spectral density. We test the universal kinematic consequences of wall fluctuations, and find good agreement with the predicted rough-wall broadening and nearby Gaussian behavior in Monte Carlo simulations of the 3D Ising model with anti-periodic boundary conditions.