Phase transitions of the q-state Potts model on multiply-laced Sierpinski gaskets

TL;DR

This paper provides an exact solution for the q-state Potts model on generalized Sierpinski fractal lattices, revealing phase transitions, multicritical points, and critical exponents through renormalization group analysis.

Contribution

It introduces an exact analytical approach to study phase transitions of the Potts model on fractal lattices, including multicritical behavior and critical exponents.

Findings

Ordered phase at low temperatures

Continuous phase transition at q>=1

Multicritical points with symmetry-breaking field

Abstract

We present an exact solution of the q-state Potts model on a class of generalized Sierpinski fractal lattices. The model is shown to possess an ordered phase at low temperatures and a continuous transition to the high temperature disordered phase at any q>=1. Multicriticality is observed in the presence of a symmetry-breaking field. Exact renormalization group analysis yields the phase diagram of the model and a complete set of critical exponents at various transitions.