Gianfelice M.
Quantum Methods for Interacting Particle Systems III, Statistical
Mechanics of Ising Models
(187K, Postcript)
ABSTRACT. We discuss the structure of the Hilbert states space of some selected
classical 2-state spin models, in the algebraic framework given in \cite
{QMIPS I}. we compute the partition function of some selected models in
terms of the eigenvalue of the associated Hamiltonian operators. In
particular we focus our attention on the ferromagnatic Ising model deriving,
in an alternative way, contour expansions which are a straightforward
extension in dimension grater than two of the classical high-temperature,
low-temperature expansions. We also obtain a different derivation of the
Fortuin-Kasteleyn representation for the Ising model involving a contour
expansion similar to the previous ones.