Dynamical behavior of a one-dimensional Ising model submitted to continuous heating and cooling processes

Abstract

The evolution of a one-dimensional Ising model with Glauber dynamics and an extrinsic energy barrier, submitted to continuous cooling and heating processes, is studied. The model is shown to exhibit many of the properties observed in real glasses. Under slow cooling, the dependence of the residual energy on the cooling law and rate is analyzed. The width of the glass transition is proportional to the inverse of the logarithm of the cooling rate. Heating processes can be studied in terms of a special solution of the master equation. Using the properties of this normal solution, the origin of the hysteresis effects when the system is cooled and reheated is discussed. The heat capacity under continuous heating presents a maximum, whose position and height can be used to characterize the thermal cycle described by the system.