Failure of Universality in Noncompact Lattice Field Theories

TL;DR

This paper demonstrates that noncompact lattice field theories can exhibit nonuniversal behavior, with critical properties depending on lattice details, challenging the traditional universality expectations in phase transition theories.

Contribution

It provides evidence that noncompact nonlinear sigma models on a lattice do not follow universal behavior, highlighting the importance of lattice specifics in critical phenomena.

Findings

Order parameter behavior varies with lattice details near criticality

Noncompact models defy traditional universality expectations

Critical behavior is sensitive to lattice definitions

Abstract

The nonuniversal behavior of two noncompact nonlinear sigma models is described. When these theories are defined on a lattice, the behavior of the order parameter (magnetization) near the critical point is sensitive to the details of the lattice definition. This is counter to experience and to expectations based on the ideas of universality.