Disordered Potts model on the diamond hierarchical lattice: Numerically exact treatment in the large-q limit

TL;DR

This paper investigates the critical behavior of the large-q limit of the disordered Potts model on a diamond hierarchical lattice, identifying phase transitions and calculating critical exponents through numerical methods.

Contribution

It provides a numerically exact analysis of phase transitions and critical exponents in the large-q disordered Potts model on a hierarchical lattice, including different disorder regimes.

Findings

Identification of ferromagnetic and paramagnetic phases.

Determination of phase transition fixed points.

Numerically exact critical exponents.

Abstract

We consider the critical behavior of the random q-state Potts model in the large-q limit with different types of disorder leading to either the nonfrustrated random ferromagnet regime or the frustrated spin glass regime. The model is studied on the diamond hierarchical lattice for which the Migdal-Kadanoff real-space renormalization is exact. It is shown to have a ferromagnetic and a paramagnetic phase and the phase transition is controlled by four different fixed points. The state of the system is characterized by the distribution of the interface free energy P(I) which is shown to satisfy different integral equations at the fixed points. By numerical integration we have obtained the corresponding stable laws of nonlinear combination of random numbers and obtained numerically exact values for the critical exponents.