Mechanism of hyperscaling violation in the 2D 8-state Potts model with long-range correlated disorder
Résumé
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. This violation is caused by large disorder fluctuations, like in the 3D random field Ising model. In the thermal sector too, evidences are given for such violation in the two hyperscaling relations $\alpha/\nu=d-2x_\epsilon$ and $1/\nu=d-x_\epsilon$. The scaling dimension of energy is conjectured to be $x_\epsilon=a/2$, where $a$ is the exponent of the algebraic decay of disorder correlations.
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