Chiral critical behavior in two dimensions from five-loop renormalization-group expansions

TL;DR

This paper investigates the critical behavior of two-dimensional N-vector spin systems with noncollinear order using five-loop renormalization-group calculations, revealing a focus-type chiral fixed point and complex crossover phenomena.

Contribution

It provides a detailed five-loop RG analysis showing the chiral fixed point differs from 1/N predictions and exhibits a focus nature, with implications for interpreting experimental and simulation results.

Findings

Chiral fixed point is a focus, not a node.

Critical behavior differs from 1/N expansion predictions.

Unusual crossover regimes mimic varying critical exponents.

Abstract

We analyse the critical behavior of two-dimensional N-vector spin systems with noncollinear order within the five-loop renormalization-group approximation. The structure of the RG flow is studied for different N leading to the conclusion that the chiral fixed point governing the critical behavior of physical systems with N = 2 and N = 3 does not coincide with that given by the 1/N expansion. We show that the stable chiral fixed point for $N \le N^*$, including N = 2 and N = 3, turns out to be a focus. We give a complete characterization of the critical behavior controlled by this fixed point, also evaluating the subleading crossover exponents. The spiral-like approach of the chiral fixed point is argued to give rise to unusual crossover and near-critical regimes that may imitate varying critical exponents seen in numerous physical and computer experiments.