Antonelli F., Isopi M.
Limit Behaviour of the Partition Function
of Spin Glasses via Stochastic Calculus
(43K, AMSTeX)
ABSTRACT. This paper studies a martingale method introduced by Comets and
Neveu for the Sherrington - Kirkpatrick model. We apply it here to a broad
class of models to get a theorem that links the convergence in distribution
of the partition function of a disordered model to the asymptotic behaviour
of the partition function of its \lq \lq ferromagnetic analogue \rq \rq.
A byproduct of this result is the deduction of the right rescaling for the
Hamiltonian of the Sherrington Kirkpatrick model with external field.
Lastly we find the equation for the critical surface delimiting the high
temperature phase for a large class of mean field spin glass models.