1303.1991 (Christophe Chatelain)

Mechanism of hyperscaling violation in the 2D 8-state Potts model with
long-range correlated disorder    [PDF]

Christophe Chatelain

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. A simple and general mechanism is presented as to how strong disorder fluctuations cause this violation. 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 hyperscaling violation exponent $\theta$ is {\sl a-priori} different for these three relations. 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.

View original: http://arxiv.org/abs/1303.1991