Monte Carlo Minimization of the Higgs-Landau Potentials

TL;DR

This paper introduces a Monte Carlo algorithm designed to identify boundary points in the orbit space, aiding in understanding symmetry breaking in Higgs and Landau potentials, demonstrated on a superconductor model.

Contribution

A novel Monte Carlo method for boundary detection in orbit spaces, applicable to Higgs and Landau potentials, enhancing analysis of symmetry breaking.

Findings

Algorithm effectively finds boundary points in orbit space.

Method successfully applied to $d$-wave superconductor Landau potential.

Robust and efficient approach demonstrated in practical case.

Abstract

We propose a Monte Carlo algorithm to search for the boundary points of the orbit space which is important in determining the symmetry breaking directions in the Higgs potential and the Landau potential. Our algorithm is robust, efficient and generally applicable. We apply the method to the Landau potential of the $d-$wave abnormal superconductor.