Two-Dimensional Heisenberg Model with Nonlinear Interactions: 1/N Corrections

TL;DR

This paper studies a 2D classical vector model with nonlinear interactions, revealing a finite-temperature transition in the Ising universality class and detailing how finite-N effects influence the critical behavior.

Contribution

It provides a large-N analysis of the model, showing the crossover from Ising to mean-field behavior and quantifying the scaling regions.

Findings

Transition belongs to the Ising universality class.

The Ising critical region scales as 1/N^{3/2} and 1/N in different directions.

Only mean-field behavior is observed at infinite N.

Abstract

We investigate a two-dimensional classical $-vector model with a generic nearest-neighbor interaction $W(\bsigma_i\cdot \bsigma_j)$ in the large-N limit, focusing on the finite-temperature transition point at which energy-energy correlations become critical. We show that this transition belongs to the Ising universality class. However, the width of the region in which Ising behavior is observed scales as $1/N^{3/2}$ along the magnetic direction and as 1/N in the thermal direction; outside a crossover to mean-field behavior occurs. This explains why only mean-field behavior is observed for $N=\infty$