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A branching process showing a phase transition

Published online by Cambridge University Press:  14 July 2016

T. Moore and
J. L. Snell
T. Moore*
Affiliation:
Marietta College
J. L. Snell*
Affiliation:
Dartmouth College
*
∗ Postal address: Marietta College, Marietta, Ohio 45750, U.S.A.
∗∗ Postal address: Department of Mathematics, Dartmouth College, Hanover, NH 03755, U.S.A.
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Abstract

It is shown that a phase transition for the Ising model on a tree graph can be detected by the limiting behavior of the magnetization. The relevant limit theorems are special cases of limit theorems for multitype branching processes.

Keywords

BRANCHING PROCESSESPHASE TRANSITIONLIMIT THEOREMSMARKOV RANDOM FIELDS

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 2 , June 1979, pp. 252 - 260
Copyright
Copyright © Applied Probability Trust 1979 

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Footnotes

The preparation of this paper was supported in part by a grant from the National Science Foundation

References

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