Dynamic scaling behavior at thermal first-order transitions in systems with disordered boundary conditions

Haralambos Panagopoulos,Ettore Vicari,Andrea Pelissetto

doi:10.1103/physrevd.98.074507

Abstract

We investigate the equilibrium and off-equilibrium behaviors of systems at thermal first-order transitions (FOTs) when the boundary conditions favor one of the two phases. As a theoretical laboratory we consider the two-dimensional Potts model. We show that an anomalous finite-size scaling emerges in systems with open boundary conditions favoring the disordered phase, associated with a mixed regime where the two phases are spatially separated. Correspondingly, if the system is slowly heated across the transition, the characteristic times of the off-equilibrium dynamics scale with a power of the size. We argue that these features generally apply to systems at FOTs, when boundary conditions favor one of the two phases. In particular, they should be relevant for the experimental search of FOTs of the quark-gluon plasma in heavy-ion collisions.

Highlights

Understanding finite-size effects at phase transitions is of great phenomenological importance, because it allows us to correctly interpret experiments and numerical investigations of finite-size systems close to the transition point, where thermodynamic quantities develop singularities in the infinite-volume limit
We show that disordered boundary conditions give rise to an offequilibrium finitesize scaling (FSS) (OFSS) characterized by a timescale increasing as a power of the size l, i.e., τðlÞ ∼ l2, instead of the usual exponentially large timescale emerging at first-order transitions (FOT)
We argue that the mechanism driving these dynamic behaviors is quite general, and that they are expected to be developed at generic thermal FOTs when the boundary conditions favor one of the two phases

Summary

Introduction

Understanding finite-size effects at phase transitions is of great phenomenological importance, because it allows us to correctly interpret experiments and numerical investigations of finite-size systems close to the transition point, where thermodynamic quantities develop singularities in the infinite-volume limit. Dynamic scaling behavior at thermal first-order transitions in systems with disordered boundary conditions

Results

Conclusion