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Moscow Mathematical Journal, 2001, Volume 1, Number 3, Pages 345–363
DOI: https://doi.org/10.17323/1609-4514-2001-1-3-345-363 (Mi mmj24) 		 
This article is cited in 30 scientific papers (total in 30 papers)

Rigidity of the critical phases on a Cayley tree

P. M. Blehera, J. Ruizb, R. H. Schonmannc, S. B. Shlosmanb, V. A. Zagrebnovd

a Department of Mathematical Sciences, Indiana University–Purdue University Indianapolis
b CNRS – Center of Theoretical Physics
c University of California, Los Angeles
d Université de la Mediterranee Aix-Marseille II
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DOI: https://doi.org/10.17323/1609-4514-2001-1-3-345-363
Abstract: We discuss statistical mechanics on nonamenable graphs, and we study the features of the phase transition, which are due to nonamenability. For the Ising model on the usual lattice it is known that below the critical temperature fluctuations of magnetization are much less likely in the states with nonzero magnetic field than in the pure states with zero field. We show that on the Cayley tree the corresponding fluctuations have the same order.
Key words and phrases: Tree, nonamenable graph, Ising model, large deviations, droplet.
Received: April 10, 2001; in revised form August 28, 2001
Bibliographic databases:
MSC: 60F10, 82B20
Language: English
Citation: P. M. Bleher, J. Ruiz, R. H. Schonmann, S. B. Shlosman, V. A. Zagrebnov, “Rigidity of the critical phases on a Cayley tree”, Mosc. Math. J., 1:3 (2001), 345–363
Citation in format AMSBIB
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\paper Rigidity of the critical phases on a~Cayley tree
\jour Mosc. Math.~J.
\yr 2001
\vol 1
\issue 3
\pages 345--363
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