Crossover phenomena involving the dense O($n$) phase

Abstract

We explore the properties of the low-temperature phase of the O($n$) loop model in two dimensions by means of transfer-matrix calculations and finite-size scaling. We determine the stability of this phase with respect to several kinds of perturbations, including cubic anisotropy, attraction between loop segments, double bonds and crossing bonds. In line with Coulomb gas predictions, cubic anisotropy and crossing bonds are found to be relevant and introduce crossover to different types of behavior. Whereas perturbations in the form of loop-loop attractions and double bonds are irrelevant, sufficiently strong perturbations of these types induce a phase transition of the Ising type, at least in the cases investigated. This Ising transition leaves the underlying universal low-temperature O($n$) behavior unaffected.

12 pages, 8 figures

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Cited by in corpus (5)

• Ising-like transitions in the O($n$) loop model on the square lattice
• Completely packed O($n$) loop models and their relation with exactly solved coloring models
• Ultrafast scattering dynamics of coherent phonons in Bi${}_{1-x}$Sb${}_x$ in the Weyl semimetal phase
• Ising-like phase transition of an n-component Eulerian face-cubic model
• Critical Line of the O($N$) Loop Model on the Square Lattice