Critical thermodynamics of three-dimensional chiral model for N > 3

TL;DR

This study analyzes the critical behavior of three-dimensional N-vector chiral models for various N, identifying two critical N values that determine whether phase transitions are continuous or first-order, and revealing complex RG flow structures.

Contribution

The paper provides new estimates for the critical N values separating different phase transition types in 3D chiral models using six-loop RG analysis.

Findings

Identified N_{c1} = 6.4(4) and N_{c2} = 5.7(3) as critical N values.

Discovered spiral-like RG flow trajectories for N between N_{c2} and N_{c1}.

Showed that physical N=2 and N=3 fall into the first-order transition domain with complex crossover behavior.

Abstract

The critical behavior of the three-dimensional $N$-vector chiral model is studied for arbitrary $N$. The known six-loop renormalization-group (RG) expansions are resummed using the Borel transformation combined with the conformal mapping and Pad\'e approximant techniques. Analyzing the fixed point location and the structure of RG flows, it is found that two marginal values of $N$ exist which separate domains of continuous chiral phase transitions $N > N_{c1}$ and $N < N_{c2}$ from the region $N_{c1} > N > N_{c2}$ where such transitions are first-order. Our calculations yield $N_{c1} = 6.4(4)$ and $N_{c2} = 5.7(3)$. For $N > N_{c1}$ the structure of RG flows is identical to that given by the $\epsilon$ and 1/N expansions with the chiral fixed point being a stable node. For $N < N_{c2}$ the chiral fixed point turns out to be a focus having no generic relation to the stable fixed point seen at small $\epsilon$ and large $N$. In this domain, containing the physical values $N = 2$ and $N = 3$, phase trajectories approach the fixed point in a spiral-like manner giving rise to unusual crossover regimes which may imitate varying (scattered) critical exponents seen in numerous physical and computer experiments.