Multicanonical ensemble: A new approach to simulate first-order phase transitions

TLDR

Using the multicanonical algorithm, we simulate the first‑order transition of the 2D 10‑state Potts model on lattices up to 100×100. The multicanonical method shows tunneling times grow only as L^2.65, yielding over two orders of magnitude speedup on the largest lattice compared to heat‑bath, and enables precise calculation of the interfacial free energy per unit area.

Abstract

Relying on the recent proposed multicanonical algorithm, we present a numerical simulation of the first-order phase transition in the 2D 10-state Potts model on lattices up to sizes 100\ifmmode\times\else\texttimes\fi{}100. It is demonstrated that the new algorithm lacks an exponentially fast increase of the tunneling time between metastable states as a function of the linear size L of the system. Instead, the tunneling time diverges approximately proportional to ${\mathit{L}}^{2.65}$. On our largest lattice we gain more than 2 orders of magnitude as compared to a standard heat-bath algorithm. As a first physical application we report a high-precision computation of the interfacial free energy per unit area.