Statistical mechanical systems on complete graphs, infinite exchangeability, finite extensions and a discrete finite moment problem
Artikel i vetenskaplig tidskrift, 2007
We show that a large collection of statistical mechanical systems with quadratically
represented Hamiltonians on the complete graph can be extended to infinite exchangeable
processes. This includes all ferromagnetic Ising, Potts and Heisenberg models. By
de Finetti's theorem, this is equivalent to showing that these probability measures can be
expressed as averages of product measures. We provide examples showing that
``ferromagnetism'' is not however in itself sufficient and also study in some detail the
Ising model with an additional 3-body interaction. Finally, we study the question of how
much the antiferromagnetic Ising model can be extended. In this direction, we obtain sharp
asymptotic results via a solution to a new moment problem. We also obtain a ``formula'' for
the extension which is valid in many cases.
discrete moment problems
statistical mechanics
infinite exchangeability