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

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 $α/ν=d-2x_\varepsilon$ and $1/ν=d-x_\varepsilon$. 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.

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