# The Roughening Transition of the 3D Ising Interface: A Monte Carlo Study

## TL;DR

This study uses a finite size scaling Monte Carlo method to precisely analyze the roughening transition of a 3D Ising interface, confirming its Kosterlitz-Thouless nature with high accuracy.

## Contribution

It introduces a refined Monte Carlo finite size scaling approach to accurately determine the Ising interface roughening transition and confirms its theoretical nature.

## Key findings

- Confirmed the Kosterlitz-Thouless nature of the transition
- Precisely estimated the inverse transition temperature as 0.40754(5)
- Achieved a two-order-of-magnitude improvement in accuracy

## Abstract

We study the roughening transition of an interface in an Ising system on a 3D simple cubic lattice using a finite size scaling method. The particular method has recently been proposed and successfully tested for various solid on solid models. The basic idea is the matching of the renormalization-group-flow of the interface with that of the exactly solvable body centered cubic solid on solid model. We unambiguously confirm the Kosterlitz-Thouless nature of the roughening transition of the Ising interface. Our result for the inverse transition temperature $K_R=0.40754(5)$ is almost by two orders of magnitude more accurate than the estimate of Mon, Landau and Stauffer.