FINITE SIZE SCALING FOR FIRST ORDER TRANSITIONS: POTTS MODEL

TL;DR

This paper tests a finite-size scaling algorithm on q-state Potts models in 2D and 3D, demonstrating its effectiveness in distinguishing first- and second-order phase transitions through Monte Carlo simulations.

Contribution

The study applies and validates a finite-size scaling method for identifying phase transition orders in Potts models, supported by Monte Carlo data and analytic calculations.

Findings

Monte Carlo data distinguish transition types effectively.

Magnetic exponent Y approaches D for large q, indicating first-order transitions.

Finite-size scaling method aligns with theoretical expectations.

Abstract

The finite-size scaling algorithm based on bulk and surface renormalization of de Oliveira (1992) is tested on q-state Potts models in dimensions D = 2 and 3. Our Monte Carlo data clearly distinguish between first- and second-order phase transitions. Continuous-q analytic calculations performed for small lattices show a clear tendency of the magnetic exponent Y = D - beta/nu to reach a plateau for increasing values of q, which is consistent with the first-order transition value Y = D. Monte Carlo data confirm this trend.