Spin and Gauge Systems on Spherical Lattices

TL;DR

This paper investigates spin and gauge systems on spherical lattices, analyzing finite size scaling and phase transitions in 2D and 4D models, including Ising, Potts, and U(1) gauge theories, revealing critical behavior and transition orders.

Contribution

It provides the first detailed finite size scaling analysis of spin and gauge models on spherical topologies, highlighting phase transition characteristics in these geometries.

Findings

Ising and Potts models behave as expected on spherical lattices

4D U(1) gauge theory shows second order phase transition with critical exponent ~0.36

Finite size scaling analysis confirms transition types in spherical topologies

Abstract

We present results for 2D and 4D systems on lattices with topology homotopic to the surface of a (hyper) sphere $S^2$ or $S^4$. Finite size scaling is studied in situations with phase transitions of first and second order type. The Ising and Potts models exhibit the expected behaviour; for the 4D pure gauge $U(1)$ theory we find consistent scaling indicative of a second order phase transition with critical exponent $\nu\simeq 0.36(1)$.