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November, 1982 Critical Phenomena for Spitzer's Reversible Nearest Particle Systems
David Griffeath, Thomas M. Liggett
Ann. Probab. 10(4): 881-895 (November, 1982). DOI: 10.1214/aop/1176993711


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.


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David Griffeath. Thomas M. Liggett. "Critical Phenomena for Spitzer's Reversible Nearest Particle Systems." Ann. Probab. 10 (4) 881 - 895, November, 1982.


Published: November, 1982
First available in Project Euclid: 19 April 2007

zbMATH: 0498.60090
MathSciNet: MR672290
Digital Object Identifier: 10.1214/aop/1176993711

Primary: 60K35
Secondary: 60J10 , 82A25

Keywords: Critical exponents , critical values , interacting particle systems , Markov chains , phase transition , Recurrence and transience , reversibility

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 4 • November, 1982
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