Phase separation in systems with absorbing states

Abstract

Abstract. -We study the problem of phase separation in systems with a positive definite order parameter, and in particular, in systems with absorbing states. Owing to the presence of a single minimum in the free energy driving the relaxation kinetics, there are some basic properties differing from standard phase separation. We study analytically and numerically this class of systems; in particular we determine the phase diagram, the growth laws in one and two dimensions and the presence of scale invariance. Some applications are also discussed.The presence of conservation laws plays a key role in determining the phenomenology and critical behavior of phase transitions both in equilibrium and nonequilibrium systems. For instance, the dynamics of models for magnetism change dramatically depending on whether the order parameter is a conserved quantity or not [1]. In the conserving case, models may exhibit phenomena such as spinodal decomposition (SD hereafter) and droplet growth via condensation-evaporation [2, 3, 4], which are absent in models with non-conserving dynamics. The problem of SD that appears, for instance in binary alloys, polymers and spin systems with conserved magnetization, have attracted a lot of interest in the last decades [2,3,4], and despite the efforts devoted to understand their phenomenology, some of their aspects remain unclear. The key issue is that of understanding the dynamics of a system quenched from a state in the homogeneous phase into a broken-symmetry phase. Depending on the value of the conserved order parameter, M , different types of morphologies can show up. The archetypal field theory representing this class of systems is the model B (or Cahn-Hilliard equation), defined by the following Langevin equationTypeset using EURO-L A T E X

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