A New Method to Determine First-Order Transition Points from Finite-Size Data

We consider a temperature driven first-order phase transition describing the coexistence of q ordered low-temperature phases and one disordered high-temperature phase at the infinite volume transition temperature T0. Analysing the exponential corrections to the usual heuristic formula of the periodic partition function in a box of volume V, Zper = ∑ m exp(−βfmV ), where β = 1/kBT and fm is the (metastable) free energy of the phase m, we propose several definitions of a finite volume transition temperature T0(V ) which involve only exponential corrections with respect to T0. We test our propositions in the d = 2 Potts model for q = 5, 8 and 10 by means of Monte Carlo simulations, using the single cluster update procedure. PACS numbers: 05.50. +q, 64.60. Pi, 75.10. Hk ∗Present address: HLRZ, Forschungszentrum Jülich, 5170 Jülich, Germany