Dense loops, supersymmetry, and Goldstone phases in two dimensions

TL;DR

This paper explores the dense-loop phases in two-dimensional models related to O(N) symmetry, revealing a Goldstone phase for -2<N<2 with crossings, supported by numerical and exact lattice model results.

Contribution

It demonstrates that the Goldstone broken-symmetry phase is generic for -2<N<2 in dense-loop models with crossings, extending previous non-crossing models.

Findings

Goldstone phase exists for -2<N<2 with loop crossings

Numerical results support the phase's existence

Exact lattice model analysis corroborates the findings

Abstract

Loop models in two dimensions can be related to O(N) models. The low-temperature dense-loops phase of such a model, or of its reformulation using a supergroup as symmetry, can have a Goldstone broken-symmetry phase for N<2. We argue that this phase is generic for -2< N <2 when crossings of loops are allowed, and distinct from the model of non-crossing dense loops first studied by Nienhuis [Phys. Rev. Lett. 49, 1062 (1982)]. Our arguments are supported by our numerical results, and by a lattice model solved exactly by Martins et al. [Phys. Rev. Lett. 81, 504 (1998)].