On phase transition and the critical size in spatially restricted systems

摘要

We study the finite-size effects on the critical temperature in spatially restricted systems with bulk second-order phase transition using the Fokker-Planck equation approach. It is established that the dependence of the transition temperature on system size is characterized by the competition of two length scales. The first scale is similar to the correlation length, determining the critical behavior in sufficiently large samples. The second scale appears as a consequence of the stochastic nature of the order parameter and controls the transitional features in small samples, particularly in the vicinity of the critical size. It is also found that the rate of the critical slowdown of relaxation of the order parameter fluctuations increases as the volume of the system decreases.