# Numerical study of the roughness of domain walls in the 2-dimensional random bond Ising model using a weighed-loop algorithm

## TL;DR

This paper introduces a weighed-loop algorithm for efficiently finding low-energy states in the 2D random bond Ising model, demonstrating improved performance over existing methods and analyzing domain wall roughness across various conditions.

## Contribution

The paper presents a novel weighed-loop algorithm applicable to any weighed graph network, optimized for exploring rough energy landscapes in the 2D random bond Ising model.

## Key findings

- The weighed-loop algorithm outperforms Niedermayer's algorithm at low temperatures and high disorder.
- High-temperature roughness behavior matches low-temperature expansion predictions.
- Temperature, disorder, and system size significantly influence domain wall roughness.

## Abstract

We introduce a weighed-loop algorithm that is applicable to any weighed graph network. It is designed to prefer a route of energetically unfavourable bonds in the lattice that can then be flipped without changing the structure inside and outside the enclosed loop. Due to this property there are effectively no energy barriers thus making this algorithm very suitable for finding low energy states in very rough energy landscapes. We apply this algorithm to the random bond Ising model with domain walls and show that the weighed-loop algorithm can outperform Niedermayer's algorithm for low enough temperatures and high enough disorder. We consolidate the high-temperature behaviour of the roughness of a domain-wall with a low-temperature expansion presented in this paper and show agreement with results from our simulations. The effects of temperature, disorder, and system size on the roughness of domain-walls is also investigated.