Locally self-similar phase diagram of the disordered Potts model on the hierarchical lattice

TL;DR

This paper investigates the critical behavior of the disordered q-state Potts model on a hierarchical lattice, revealing a self-similar phase boundary characterized by a logarithmic spiral and suggesting complex reentrant phase phenomena.

Contribution

It introduces a renormalization group analysis of the large-q disordered Potts model, uncovering a self-similar phase boundary near the multicritical point.

Findings

Phase boundary is a logarithmic spiral.

Infinite reentrances in the thermodynamic limit.

Standard thermodynamic phases cannot be defined in this region.

Abstract

We study the critical behavior of the random q-state Potts model in the large-q limit on the diamond hierarchical lattice with an effective dimensionality $d_{\rm eff} > 2$. By varying the temperature and the strength of the frustration the system has a phase transition line between the paramagnetic and the ferromagnetic phases which is controlled by four different fixed points. According to our renormalization group study the phase-boundary in the vicinity of the multicritical point is self-similar, it is well represent ed by a logarithmic spiral. We expect infinite number of reentrances in the thermodynamic limit, consequently one can not define standard thermodynamic phases in this region.