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Abstract: We analyze the properties of the contact process with long-range interactionsby the use of a kinetic ensemble in which the total number of particles isstrictly conserved. In this ensemble, both annihilation and creation processesare replaced by an unique process in which a particle of the system chosen atrandom leaves its place and jumps to an active site. The present approach isparticularly useful for determining the transition point and the nature of thetransition, whether continuous or discontinuous, by evaluating the fractaldimension of the cluster at the emergence of the phase transition. We alsopresent another criterion appropriate to identify the phase transition thatconsists of studying the system in the supercritical regime, where the presenceof a -loop- characterizes the first-order transition. All results obtained bythe present approach are in full agreement with those obtained by using theconstant rate ensemble, supporting that, in the thermodynamic limit the resultsfrom distinct ensembles are equivalent.



Author: Carlos E. Fiore, Mário J. de Oliveira

Source: https://arxiv.org/



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