  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.
