Critical Phenomena for Spitzer's Reversible Nearest Particle Systems
Griffeath, David ; Liggett, Thomas M.
Ann. Probab., Tome 10 (1982) no. 4, p. 881-895 / Harvested from Project Euclid
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Motivated by several results and open problems concerning Harris' basic contact process, we consider the relationship between the critical behavior of the finite and infinite versions of Spitzer's reversible nearest particle systems. We show that the critical values for the finite and infinite systems agree, but that the behavior of the two systems at the common critical value can differ. The Nash-Williams recurrence criterion for reversible Markov chains is an important tool used in the proofs of the main results, and we give a new treatment of that theory. Finally, we compute several critical exponents for the nearest particle systems.
Publié le : 1982-11-14
Classification:  Interacting particle systems,  critical values,  Markov chains,  recurrence and transience,  reversibility,  phase transition,  critical exponents,  60K35,  60J10,  82A25 
@article{1176993711,
     author = {Griffeath, David and Liggett, Thomas M.},
     title = {Critical Phenomena for Spitzer's Reversible Nearest Particle Systems},
     journal = {Ann. Probab.},
     volume = {10},
     number = {4},
     year = {1982},
     pages = { 881-895},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176993711}
}

Griffeath, David; Liggett, Thomas M. Critical Phenomena for Spitzer's Reversible Nearest Particle Systems. Ann. Probab., Tome 10 (1982) no. 4, pp.  881-895. http://gdmltest.u-ga.fr/item/1176993711/