Magnetization bound for classical spin models on graphs

Details Magnetization bound for classical spin models on graphs Magnetization bound for classical spin models on graphs

1998-08-05

arxiv.org/abs/cond-mat/9808046v1

Physics

Condensed Matter

Statistical Mechanics

14 pages

Scientific paper

In this paper we prove the existence of phase transitions at finite temperature for O(n) classical ferromagnetic spin models on infrared finite graphs. Infrared finite graphs are infinite graphs with $\lim {m\to 0^+} {\bar Tr (L+m)^{-1} < \infty$, where $L$ is the Laplacian operator of the graph. The ferromagnetic couplings are only requested to be bounded by two positive constants. The proof, inspired by the classical result of Fr\"ohlich, Simon and Spencer on lattices, is given through a rigorous bound on the average magnetization. The result holds for $n\ge 1$ and it includes as a particular case the Ising model.

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