Critical and tricritical singularities of the three-dimensional random-bond Potts model for large $q$

TL;DR

This paper investigates how bond randomness affects the phase transition in the three-dimensional large-q Potts model, identifying a tricritical point and analyzing critical exponents for different regimes.

Contribution

It introduces the concept of a tricritical disorder in the 3D large-q Potts model and estimates associated critical exponents, showing their independence from disorder strength.

Findings

Identification of a tricritical disorder point separating transition regimes

Estimation of tricritical exponents $eta_t/ u_t=0.10(2)$ and $ u_t=0.67(4)$

Confirmation of disorder-independent critical exponents in the second-order regime

Abstract

We study the effect of varying strength, $\delta$, of bond randomness on the phase transition of the three-dimensional Potts model for large $q$. The cooperative behavior of the system is determined by large correlated domains in which the spins points into the same direction. These domains have a finite extent in the disordered phase. In the ordered phase there is a percolating cluster of correlated spins. For a sufficiently large disorder $\delta>\delta_t$ this percolating cluster coexists with a percolating cluster of non-correlated spins. Such a co-existence is only possible in more than two dimensions. We argue and check numerically that $\delta_t$ is the tricritical disorder, which separates the first- and second-order transition regimes. The tricritical exponents are estimated as $\beta_t/\nu_t=0.10(2)$ and $\nu_t=0.67(4)$. We claim these exponents are $q$ independent, for sufficiently large $q$. In the second-order transition regime the critical exponents $\beta_t/\nu_t=0.60(2)$ and $\nu_t=0.73(1)$ are independent of the strength of disorder.