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 ${\mathit{T}}_0$. Analyzing the exponential corrections to the periodic partition function in a box of volume V, ${\mathit{Z}}_{\mathrm{per}}$=${\mathit{tsum}}_{\mathit{m}}$ exp(-β${\mathit{f}}_{\mathit{m}}$V), where ${\mathit{f}}_{\mathit{m}}$ is the (metastable) free energy of the phase m, we propose several definitions of a finite-volume transition temperature ${\mathit{T}}_0$(V) which involve only exponential corrections with respect to ${\mathit{T}}_0$. 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.