First-order and pseudo-first-order transition in the high dimensional $O(N)\otimes O(M)$ model

TL;DR

This paper uses the renormalization group to analyze high-dimensional $O(N) imes O(M)$ models, revealing conditions for first and second order phase transitions, including pseudo-first-order behavior, with specific results for certain lattice models.

Contribution

It provides a detailed RG analysis of the $O(N) imes O(M)$ model in high dimensions, identifying the nature of phase transitions and highlighting cases with first-order behavior.

Findings

Transitions can be first or second order for $N \\geq M \\geq 2$.

Pseudo-first-order behavior is possible in dimensions greater than four.

Specific lattice models exhibit clear first-order transitions.

Abstract

Using the renormalization group approach, we consider the $O(N)\otimes O(M)$ model in four and more dimensions. We find that independently on $N$ and $M$, for $N\geq M\geq 2$, a transition can be of both the first and second order. In $d>4$, we also cannot exclude a pseudo-first-order behavior. As specific physically interesting cases, we consider the lattice version of the $O(2)\otimes O(2)$, $O(3)\otimes O(2)$ and $O(3)\otimes O(3)$ sigma models on a four dimensional hypercubic lattice. In all these cases, we find a distinct first-order transition.