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

Christophe Chatelain (1, 2)

1 IJL - Institut Jean Lamour
2 IISER TVM - Indian Institute of Science Education and Research Thiruvananthapuram

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.

Mots clés: Hyperscaling violation; Potts model; Disorder; Monte Carlo simulation

Domaines: Mécanique statistique [cond-mat.stat-mech]

Christophe Chatelain. Hyperscaling violation in the 2D 8-state Potts model with long-range correlated disorder. EPL - Europhysics Letters, 2013, 102, pp.66007. ⟨10.1209/0295-5075/102/66007⟩. ⟨hal-00798317v3⟩