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

School of Physics, Indian Institute of Science Education and Research (IISER) - Thiruvananthapuram, India and Groupe de Physique Statistique, Département P2M, Institut Jean Lamour (CNRS UMR 7198), Université de Lorraine - F-54506 Vandoeuvre les Nancy, France, EU

Received: 21 March 2013
Accepted: 10 June 2013

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 − 2x_σ 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 − 2x_ε and 1/ν = d − x_ε. 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_ε = a/2, where a is the exponent of the algebraic decay of disorder correlations.