Critical dynamics of nonconserved $N$-vector model with anisotropic nonequilibrium perturbations

TL;DR

This paper investigates the critical dynamics of nonconserved N-vector models with spatial-anisotropic bias perturbations, revealing conditions for single length scale behavior and identifying rich universality classes for N=3.

Contribution

It establishes the conditions under which anisotropic nonconserving N-vector models exhibit single length scale behavior and constructs new field theories for N=3 with diverse critical phenomena.

Findings

No single length scale for N=2 or N≥4 models, leading to Ising universality.

Existence of nontrivial field theories for N=3 with complex critical behavior.

Identification of two distinct universality classes for N=3 systems.

Abstract

We study dynamic field theories for nonconserving $N$-vector models that are subject to spatial-anisotropic bias perturbations. We first investigate the conditions under which these field theories can have a single length scale. When N=2 or $N \ge 4$, it turns out that there are no such field theories, and, hence, the corresponding models are pushed by the bias into the Ising class. We further construct nontrivial field theories for N=3 case with certain bias perturbations and analyze the renormalization-group flow equations. We find that the three-component systems can exhibit rich critical behavior belonging to two different universality classes.