Spin models on Platonic solids and asymptotic freedom

TL;DR

This paper investigates a two-dimensional sigma-model with icosahedral/dodecahedral symmetry, revealing through numerical analysis that its continuum limit differs from the traditional O(3) sigma-model, indicating unique asymptotic behavior.

Contribution

It provides high-precision numerical evidence that sigma-models with Platonic solid symmetries have distinct continuum limits from O(3) models, highlighting new aspects of asymptotic freedom.

Findings

Continuum limit differs from O(3) sigma-model

High-precision finite-size numerical results obtained

Symmetry impacts the asymptotic behavior of the model

Abstract

We consider a two-dimensional sigma-model with discrete icosahedral/dodecahedral symmetry. We present high-precision finite-size numerical results that show that the continuum limit of this model is different from the continuum limit of the rotationally invariant O(3) sigma-model.