Geometric methods for the most general Ginzburg-Landau model with two order parameters

TL;DR

This paper introduces a geometric approach to analyze the complex Ginzburg-Landau model with two order parameters, enabling easier minimization of the Landau potential and providing deeper insights into the model's properties.

Contribution

A novel geometric method is developed to simplify the minimization of the Ginzburg-Landau potential with two order parameters, overcoming algebraic challenges.

Findings

The geometric approach facilitates the analysis of the Landau potential.

It provides new insights into the properties of the two-parameter Ginzburg-Landau model.

The method improves understanding of phase transitions in the model.

Abstract

The Landau potential in the general Ginzburg-Landau theory with two order parameters and all possible quadratic and quartic terms cannot be minimized with the straightforward algebra. Here, a geometric approach is presented that circumvents this computational difficulty and allows one to get insight into many properties of the model in the mean-field approximation.