Polymer growth in solution and the dynamic epidemic model: dimensionality and critical exponents

Abstract

Recent interest in solutions of the static and dynamic epidemic models has led us to reconsider some features of the critical exponents of these models. In particular, our starting point is that the known values of such exponents take different values depending on dimensionality d, for dynamic epidemics, depending also on the looped nature of the chain, but the universality is regained for d > 1. According to this superuniversality property for d > 1, we could predict that the critical exponents γ and ν for dynamic epidemics on a square lattice should be 43/18 and 4/3, respectively. Furthermore, from numerical results in literature, we predict the critical exponents for the Potts model in three dimensions and the percolation exponents (q = 1) for d = 1, 2, 3, 4, 5 and d ≥ 6. Other areas of relevance beyond that in the title embrace conduction in heterogeneous media as well as a description of the spreading of a fluid in a medium possessing mobile impurities.