Monte-Carlo Study of Pure-Phase Cumulants of 2D q-State Potts Models

We performed Monte-Carlo simulations of the two-dimensional $q$-state Potts model with $q=10$, 15, and 20 to study the energy and magnetization cumulants in the ordered and disordered phase at the first-order transition point $\beta_{\rm t}$. By using very large systems of size $300\times 300$, $120\times 120$, and $80\times 80$ for $q=10$, 15, and 20, respectively, our numerical estimate provide practically (up to unavoidable, but very small statistical errors) exact results which can serve as a useful test of recent resummed large-$q$ expansions for the energy cumulants by Bhattacharya et al. J. Phys. France 7 (1997) 81). Up to the third-order cumulant and down to $q=10$ we obtain very good agreement, and also the higher-order estimates are found to be compatible