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**Harvard**

Liggett, T., Steif, J. och Toth, B. (2007) *Statistical mechanical systems on complete graphs, infinite exchangeability, finite extensions and a discrete finite moment problem*.

** BibTeX **

@article{

Liggett2007,

author={Liggett, Thomas and Steif, Jeffrey and Toth, Balint},

title={Statistical mechanical systems on complete graphs, infinite exchangeability, finite extensions and a discrete finite moment problem},

journal={Annals of Probability},

issn={0091-1798},

volume={35},

issue={3},

pages={867-914},

abstract={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. },

year={2007},

keywords={statistical mechanics, infinite exchangeability,discrete moment problems},

}

** RefWorks **

RT Journal Article

SR Print

ID 62395

A1 Liggett, Thomas

A1 Steif, Jeffrey

A1 Toth, Balint

T1 Statistical mechanical systems on complete graphs, infinite exchangeability, finite extensions and a discrete finite moment problem

YR 2007

JF Annals of Probability

SN 0091-1798

VO 35

IS 3

SP 867

OP 914

AB 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.

LA eng

DO 10.1214/009117906000001033

OL 30