Chiral phase transitions: focus driven critical behavior in systems with planar and vector ordering

TL;DR

This paper demonstrates that the critical behavior of N-vector chiral models for N=2, 3 is governed by a stable focus fixed point, leading to spiral-like approaches and unusual crossover phenomena in 2D and 3D.

Contribution

It provides high-order renormalization-group analysis showing the stable focus nature of the chiral fixed point for physical N values in both two and three dimensions.

Findings

Stable focus fixed point in 2D and 3D for N=2, 3

Spiral-like approach causes unusual crossover regimes

Near-critical regimes mimic varying critical exponents

Abstract

The fixed point that governs the critical behavior of magnets described by the $N$-vector chiral model under the physical values of $N$ ($N =2, 3$) is shown to be a stable focus both in two and three dimensions. Robust evidence in favor of this conclusion is obtained within the five-loop and six-loop renormalization-group analysis in fixed dimension. The spiral-like approach of the chiral fixed point results in unusual crossover and near-critical regimes that may imitate varying critical exponents seen in physical and computer experiments.