Two Dimensional Poincare Maps constructed through Ginzburg-Landau Theory of critical phenomena in Physics

TL;DR

This paper constructs two-dimensional Poincare maps based on Ginzburg-Landau theory to describe symmetry breaking and tricritical crossover phenomena, with numerical verification confirming their accuracy near critical points.

Contribution

It introduces a novel method of using Poincare maps derived from Ginzburg-Landau theory to analyze critical phenomena in physics.

Findings

Phase space diagrams match theoretical predictions.

Maps are accurate near critical points.

Numerical experiments verify the maps' correctness.

Abstract

Based on the saddle point approximation in G-L theory of the critical phenomena we construct two-dimensional Poincare maps which describe the symmetry breaking (SB) and the tricritical crossover phenomenon in Physics. The phase space diagrams of these maps are in agreement with the theoretical predictions. A correction in these maps close to the critical point for small values of the order parameter is attempted. Finally we demonstrate that numerical experiments verify the correctness of these maps.