Magnetization bound for classical spin models on
graphs
Alessandro Vezzani
Abstract
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.
Elenco dei partecipanti al convegno di Bari.