Limit Behaviour of the Partition Function of Spin Glasses via Stochastic Calculus
نویسنده
چکیده
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 \ferromagnetic analogue ". A byproduct of this result is the deduction of the right rescaling for the Hamiltonian of the Sherrington Kirkpatrick model with external eld. Lastly we nd the equation for the critical surface delimiting the high temperature phase for a large class of mean eld spin glass models.
منابع مشابه
Griffiths Singularities in the Dynamics of Disordered Ising
We study the asymptotic behaviour of the correlation function q(t)= l N =-(Si(0) Si@>) for dilute, short-range Ising ferromagnets and spin glasses with single spin-N i-1 flip dynamics, Using an eigenfunction expansion for the time evolution operator and a variational estimate for the gap in the spectrum of this operator, we prove that, for a range of temperatures above the T, of the random syst...
متن کاملDistribution of Lee-Yang zeros and Griffiths singularities in the ±J model of spin glasses
We investigate the distribution of zeros of the partition function of the twoand three-dimensional symmetric ±J Ising spin glasses on the complex field plane. We use the method to analytically implement the idea of numerical transfer matrix which provides us with the exact expression of the partition function as a polynomial of fugacity. The results show that zeros are distributed in a wide reg...
متن کاملOn the stochastic calculus method for spins systems
In this note, we show how to generalize the stochastic calculus method introduced by Comets and Neveu [3] for two models of spin glasses, namely the SK model with external field and the perceptron model. This method allows to derive quite easily some fluctuation results for the free energy in those two cases.
متن کاملروش انتگرال مسیر برای مدل هابارد تک نواره
We review various ways to express the partition function of the single-band Hubard model as a path integral. The emphasis is made on the derivation of the action in the integrand of the path integral and the results obtained from this approach are discussed only briefly. Since the single-band Hubbard model is a pure fermionic model on the lattice and its Hamiltonian is a polynomial in creat...
متن کاملA Dynamic Programming Approach to the Parisi Functional
G. Parisi predicted an important variational formula for the thermodynamic limit of the intensive free energy for a class of mean field spin glasses. In this paper, we present an elementary approach to the study of the Parisi functional using stochastic dynamic programing and semi-linear PDE. We give a derivation of important properties of the Parisi PDE avoiding the use of Ruelle Probability C...
متن کامل