Three-Dimensional 3-State Potts Model Revisited With New Techniques

TLDR: In this paper, a detailed finite-size scaling analysis of the first-order phase transition in the 3-state Potts model on cubic lattices with emphasis on recently introduced quantities whose infinite-volume extrapolations are governed 'only' by exponentially small terms is presented.

Abstract: We report a fairly detailed finite-size scaling analysis of the first-order phase transition in the three-dimensional 3-state Potts model on cubic lattices with emphasis on recently introduced quantities whose infinite-volume extrapolations are governed `only' by exponentially small terms. In these quantities no asymptotic power series in the inverse volume are involved which complicate the finite-size scaling behaviour of standard observables related to the specific-heat maxima or Binder-parameter minima. Introduced initially for strong first-order phase transitions in q-state Potts models with ``large enough'' q, the new techniques prove to be surprisingly accurate for a q value as small as 3. On the basis of the high-precision Monte Carlo data of Alves `et al.' [Phys. Rev. B43 (1991) 5846], this leads to a refined estimate of $\beta_t = 0.550,565(10)$ for the infinite-volume transition point.