# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1904.05194