Finite-size effects in the rough phase of the 3d Ising model

TL;DR

This paper investigates finite-size effects on interfacial properties of the 3D Ising model using Monte Carlo simulations, comparing results with capillary-wave theory and effective string models.

Contribution

It provides a detailed analysis of finite-size effects in the rough phase of the 3D Ising model, incorporating comparisons with theoretical predictions.

Findings

Finite-size effects depend on the ratio of system dimensions.

Results align with capillary-wave theory in certain regimes.

Effective string models offer additional insights into interfacial fluctuations.

Abstract

Using Monte Carlo simulations, finite-size effects of interfacial properties in the rough phase of the Ising on a cubic lattice with $L\times L\times R$ sites are studied. In particular, magnetization profiles perpendicular to the flat interface of size L$\times$R are studied, with $L$ being considerably larger than $R$, in the (pre)critical temperature range. The resulting $R$-dependences are compared with predictions of the standard capillary-wave theory, in the Gaussian approximation, and with a field theory based on effective string actions, for $L$=$\infty$.