The Annals of Applied Probability

Lack of monotonicity in ferromagnetic Ising model phase diagrams

Roberto H. Schonmann and Nelson I. Tanaka

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We study patterns of the phase diagram of ferromagnetic Ising models on graphs under an external magnetic field. We provide an example of a tree with only two types of vertices on which for a range of values of the external field there is a unique Gibbs distribution at low enough and at high enough temperatures, while at intermediate temperatures there is phase coexistence (in other words, a reentrance transition takes place).

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Ann. Appl. Probab., Volume 8, Number 1 (1998), 234-245.

First available in Project Euclid: 29 July 2002

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82B27: Critical phenomena

Ising model ferromagnetism graphs phase diagram monotonicity reentrance transition


Schonmann, Roberto H.; Tanaka, Nelson I. Lack of monotonicity in ferromagnetic Ising model phase diagrams. Ann. Appl. Probab. 8 (1998), no. 1, 234--245. doi:10.1214/aoap/1027961042.

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