# Diffusion of interface and heat conduction in the three-dimensional Ising model

## TL;DR

This study explores how heat conduction and interface diffusion relate to the roughening transition in the 3D Ising model, revealing a crossover in diffusion behavior linked to the roughening transition temperature.

## Contribution

It provides numerical evidence of the connection between heat flow, interface diffusion, and the roughening transition in the 3D Ising model, suggesting heat conduction may shift the transition temperature.

## Key findings

- Diffusion constant exhibits a temperature-dependent crossover.
- Crossover temperature matches the roughening transition in equilibrium.
- Heat flow causes deviation from the equilibrium roughening transition temperature.

## Abstract

We investigate the relationship between a diffusive motion of an interface, heat conduction, and the roughening transition in the three-dimensional Ising model. We numerically compute the thermal conductivity and the diffusion constant and find that the diffusion constant shows a crossover in its temperature dependence. The crossover temperature is equal to the roughening transition temperature in equilibrium and deviates from it when heat flows in the system. From these results, we discuss the possibility that heat conduction causes a shift of the roughening transition temperature.