Critical behavior of frustrated spin systems with nonplanar orderings

TL;DR

This study investigates the critical behavior of frustrated spin systems with nonplanar orderings using a six-loop field theory approach, finding no stable fixed point for certain parameters, which suggests a first-order phase transition.

Contribution

It provides a detailed six-loop analysis of the critical behavior in frustrated spin systems with nonplanar orderings, including the determination of large-order behavior and the critical N line.

Findings

No stable fixed point for N=M=3, indicating a likely first-order transition.

Large N behavior analyzed for M=3, 4, 5.

Critical N line N_c(d=3,M) computed.

Abstract

The critical behavior of frustrated spin systems with nonplanar orderings is analyzed by a six-loop study in fixed dimension of an effective O$(N) \times $O$(M)$ Landau-Ginzburg-Wilson Hamiltonian. For this purpose the large-order behavior of the field theoretical expansion is determined. No stable fixed point is found in the physically interesting case of $M=N=3$, suggesting a first-order transition in this system. The large $N$ behavior is analyzed for $M=3, 4, 5$ and the line $N_c(d=3,M)$ which limits the region of second-order phase transition is computed.