Simulated Annealing for Topological Solitons

TL;DR

This paper introduces a simulated annealing approach to find minimal energy configurations of topological solitons in various field theories, providing an alternative to traditional differential equation methods.

Contribution

It demonstrates the application of simulated annealing to multiple nonlinear field theories, offering a new computational technique for soliton solutions.

Findings

Confirmed results consistent with standard minimization methods

Successfully applied to sine-Gordon, baby Skyrme, and nuclear Skyrme models

Provided detailed implementation of the annealing algorithm

Abstract

The search for solutions of field theories allowing for topological solitons requires that we find the field configuration with the lowest energy in a given sector of topological charge. The standard approach is based on the numerical solution of the static Euler-Lagrange differential equation following from the field energy. As an alternative, we propose to use a simulated annealing algorithm to minimize the energy functional directly. We have applied simulated annealing to several nonlinear classical field theories: the sine-Gordon model in one dimension, the baby Skyrme model in two dimensions and the nuclear Skyrme model in three dimensions. We describe in detail the implementation of the simulated annealing algorithm, present our results and get independent confirmation of the studies which have used standard minimization techniques.