Microcanonical simulation of first-order phase transitions in finite volumes

Alfred H�ller

Wolfhard Janke E

Hans Behringer, Michel Pleimling

The appearance of a convex dip in the microcanonical entropy of finite systems usually signals a first order transition. However, a convex dip also shows up in some systems with a continuous transition as, for example, in the Baxter-Wu model and in the four-state Potts model in two dimensions. We demonstrate that the appearance of a convex dip in those cases can be traced back to a finite-size effect. The properties of the dip are markedly different from those associated with a first order transition and can be understood within a microcanonical finite-size scaling theory for continuous phase transitions. Results obtained from numerical simulations corroborate the predictions of the scaling theory.

E. Praveen, S. V. M. Satyanarayana

Traditional definition of phase transition involves an infinitely large system in thermodynamic limit. Finite systems such as biological proteins exhibit cooperative behavior similar to phase transitions. We employ recently discovered analysis of inflection points of microcanonical entropy to estimate the transition temperature of the phase transition in q state Potts model on a finite two dimensional square lattice for q=3 (second order) and q=8 (first order). The difference of energy density of states (DOS) Δ ln g(E) = ln g(E+ ΔE) −ln g(E) exhibits a point of inflexion at a value corresponding to inverse transition temperature. This feature is common to systems exhibiting both first as well as second order transitions. While the difference of DOS registers a monotonic variation around the point of inflexion for systems exhibiting second order transition, it has an S-shape with a minimum and maximum around the point of inflexion for the case of first order transition.

Alain H. Billoire, R. Lacaze, André Morel

Víctor Martín-Mayor

A simple microcanonical strategy for the simulation of first-order phase transitions is proposed. At variance with flat-histogram methods, there is no iterative parameters optimization nor long waits for tunneling between the ordered and the disordered phases. We test the method in the standard benchmark: the Q-states Potts model (Q=10 in two dimensions and Q=4 in D=3). We develop a cluster algorithm for this model, obtaining accurate results for systems with more than 10(6) spins.