Boundary critical behaviour of two-dimensional random Potts models

TL;DR

This study investigates the boundary critical behavior of two-dimensional random Potts models with varying q, analyzing phase transitions, critical exponents, and multifractal properties using Monte Carlo simulations and conformal field theory.

Contribution

It provides the first detailed analysis of boundary critical exponents and multifractal behavior in random Potts models for 3≤q≤8, combining numerical and theoretical approaches.

Findings

Critical exponents increase monotonously with q.

Surface and bulk magnetizations follow expected scaling laws.

Multifractal analysis reveals complex boundary behavior.

Abstract

We consider random q-state Potts models for $3\le q \le 8$ on the square lattice where the ferromagnetic couplings take two values $J_1>J_2$ with equal probabilities. For any q the model exhibits a continuous phase transition both in the bulk and at the boundary. Using Monte Carlo techniques the surface and the bulk magnetizations are studied close to the critical temperature and the critical exponents $\beta_1$ and $\beta$ are determined. In the strip-like geometry the critical magnetization profile is investigated with free-fixed spin boundary condition and the characteristic scaling dimension, $\beta_1/\nu$, is calculated from conformal field theory. The critical exponents and scaling dimensions are found monotonously increasing with q. Anomalous dimensions of the relevant scaling fields are estimated and the multifractal behaviour at criticality is also analyzed.