Abstract
Critical properties of systems exhibiting phase transitions into phases with infinite numbers of absorbing states are studied. We analyze a non-Markovian Langevin equation recently proposed to describe the critical behavior of such systems, and also introduce and study a non-Markovian discrete model, which is argued to present the same critical features. On the basis of mean-field analysis, Monte Carlo simulations, and theoretical arguments, we conclude that the phenomenology of the non-Markovian models closely parallels that of systems with many absorbing states in one and two dimensions. The “bulk” or “static” critical properties of these systems fall in the directed percolation (DP) universality class. By contrast, the critical properties associated with the spread of an initially localized seed exhibit a more complex behavior: Depending on parameter values they can, both in one and two dimensions, fall either in the dynamical percolation or DP universality class, or else exhibit apparently nonuniversal exponents. In contrast to previous results, however, the nonuniversal exponents in 2D are found to satisfy a scaling law which implies that a particular linear combination of them is universal and assumes DP values. These results demonstrate the efficacy of the non-Markovian approach for understanding systems with many absorbing states, which are difficult to analyze in their original microscopic formulation.
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Muñoz, M.A., Grinstein, G. & Dickman, R. Phase Structure of Systems with Infinite Numbers of Absorbing States. Journal of Statistical Physics 91, 541–569 (1998). https://doi.org/10.1023/A:1023021409588
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DOI: https://doi.org/10.1023/A:1023021409588