Hyperscaling violation in the 2D 8-state Potts model with long-range correlated disorder

TL;DR

This study demonstrates that long-range correlated disorder in the 2D 8-state Potts model causes hyperscaling violations and rounds the first-order phase transition, with Monte Carlo simulations revealing new critical behavior and violation of traditional scaling relations.

Contribution

It provides the first detailed analysis of hyperscaling violations in the 2D Potts model with long-range correlated disorder, highlighting differences from uncorrelated disorder and related models.

Findings

Hyperscaling relations are violated in the presence of correlated disorder.

Disorder fluctuations induce hyperscaling violations similar to 3D random-field Ising model.

Multiple hyperscaling violation exponents are necessary to describe the system.

Abstract

The first-order phase transition of the two-dimensional eight-state Potts model is shown to be rounded when long-range correlated disorder is coupled to energy density. Critical exponents are estimated by means of large-scale Monte Carlo simulations. In contrast to uncorrelated disorder, a violation of the hyperscaling relation $\gamma/\nu=d-2x_\sigma$ is observed. Even though the system is not frustrated, disorder fluctuations are strong enough to cause this violation in the very same way as in the 3D random-field Ising model. In the thermal sector too, evidence is given for such violation in the two hyperscaling relations $\alpha/\nu=d-2x_\varepsilon$ and $1/\nu=d-x_\varepsilon$. In contrast to the random field Ising model, at least two hyperscaling violation exponents are needed. The scaling dimension of energy is conjectured to be $x_\varepsilon=a/2$, where $a$ is the exponent of the algebraic decay of disorder correlations.