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

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 γ/ν = d − 2xσ 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 α/ν = d − 2xε and 1/ν = d − xε. 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 xε = a/2, where a is the exponent of the algebraic decay of disorder correlations.