Large-n Critical Behavior of O(n)xO(m) Spin Models

TL;DR

This paper analyzes the critical behavior of O(n) x O(m) symmetric spin models using epsilon expansions and large-n techniques, providing detailed critical exponents and fixed-point structures for high-dimensional systems.

Contribution

It offers the first comprehensive calculation of critical exponents for O(n) x O(m) models at large n and across dimensions 2<d<4 using epsilon expansions and sigma models.

Findings

Critical exponents computed to O(n^{-2}) and O(3;^3) in epsilon expansion.

Fixed points and exponents determined to O(3;^2) in the 3; expansion.

General conclusions on fixed-point structure for large n and 2<d<4.

Abstract

We consider the Landau-Ginzburg-Wilson Hamiltonian with O(n)x O(m) symmetry and compute the critical exponents at all fixed points to O(n^{-2}) and to O(\epsilon^3) in a \epsilon=4-d expansion. We also consider the corresponding non-linear sigma model and determine the fixed points and the critical exponents to O(\tilde{\epsilon}^2) in the \tilde{\epsilon}=d-2 expansion. Using these results, we draw quite general conclusions on the fixed-point structure of models with O(n)xO(m) symmetry for n large and all 2 < d < 4.