Glassy behavior in a simple model with entropy barriers

Abstract

We study the dynamical behavior of a system with a variable number of particles n. The empty state n=0 is the ground state, while all the other states n>0 are degenerate in energy. In equilibrium, the mean number of particles is equal to unity, independently of the temperature. The static properties are the same as for the Backgammon model recently proposed by Ritort [Phys. Rev. Lett. 75, 1190 (1995)], while a variation of the kinetics is considered. The elementary dynamical processes are the arrival and departure of a particle. The rate of the departure process is constant, while the arrival rate is obtained from the detailed balance condition. Thus, there is no energy barrier separating the ground state n=0. Nevertheless, glassy behavior appears due to the presence of effective entropy barriers. At low temperatures, the response functions are shown to obey φ(t)≃exp[-(t/τ)γ]. In thermal cycles of cooling and reheating from low temperatures, the system shows hysteresis, which follows from the trend of the system to approach the normal curve characterizing the heating program.