A branching process showing a phase transition

1 June 1979

journal article
Published by Cambridge University Press (CUP) in Journal of Applied Probability

Vol. 16 (2) , 252-260
https://doi.org/10.2307/3212894

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

This publication has 9 references indexed in Scilit:

Markov Random Fields on an Infinite Tree
The Annals of Probability, 1975
New Type of Phase Transition
Physical Review Letters, 1974
Gibbs States on Countable Sets
Published by Cambridge University Press (CUP) ,1974
Infinite Susceptibility without Spontaneous Magnetization: Exact Properties of the Ising Model on the Cayley Tree
Progress of Theoretical Physics, 1974
Additional Limit Theorems for Indecomposable Multidimensional Galton-Watson Processes
The Annals of Mathematical Statistics, 1966
Peierls Proof of Spontaneous Magnetization in a Two-Dimensional Ising Ferromagnet
Physical Review B, 1964
The Theory of Branching Processes
Published by Springer Nature ,1963
On Ising's model of ferromagnetism
Mathematical Proceedings of the Cambridge Philosophical Society, 1936
Beitrag zur Theorie des Ferromagnetismus
Zeitschrift für Physik, 1925