ISSN:
1434-6036
Keywords:
PACS. 64.60.Ak Renormalization-group, fractal, and percolation studies of phase transitions - 64.60.Ht Dynamic critical phenomena - 05.40.+j Fluctuation phenomena, random processes, and Brownian motion
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract: We consider two stochastic processes, the Gribov process and the general epidemic process, that describe the spreading of an infectious disease. In contrast to the usually assumed case of short-range infections that lead, at the critical point, to directed and isotropic percolation respectively, we consider long-range infections with a probability distribution decaying in d dimensions with the distance as . By means of Wilson's momentum shell renormalization-group recursion relations, the critical exponents characterizing the growing fractal clusters are calculated to first order in an -expansion. It is shown that the long-range critical behavior changes continuously to its short-range counterpart for a decay exponent of the infection .
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s100510050596
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