Competing interactions and the Lifshitz-type Nonlinear Sigma Model

TL;DR

This paper demonstrates the equivalence between a quantum spherical model with competing interactions and a Lifshitz-type nonlinear sigma model, analyzing its renormalization and phase transition properties in various dimensions.

Contribution

It establishes a connection between the quantum spherical model and Lifshitz-type nonlinear sigma models, exploring their renormalization and fixed points.

Findings

Identification of nontrivial fixed points in various dimensions

Connection between phase transitions and fixed points

Analysis of renormalization properties in the 1/N expansion

Abstract

We establish the equivalence between the continuum limit of the quantum spherical model with competing interactions, which is relevant to the investigation of Lifshitz points, and the O(N) nonlinear sigma model with the addition of higher order spatial derivative operators, which breaks the Lorentz symmetry and is known as Lifshitz-type (or anisotropic) nonlinear sigma model. In the context of the 1/N expansion, we also discuss the renormalization properties of this nonlinear sigma model and find the nontrivial fixed points of the beta-functions in various dimensions, which turn out to be connected with the existence of phase transitions in the quantum spherical model.