G.A. Raggio and R.F. Werner: "The Gibbs variational principle for inhomogeneous mean field systems", Helv.Phys.Acta 64 (1991) 633--667 Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
The Classical Limit of Quantum Theory - Werner (1995) Self-citation (Werner) (Correct)
....approach based on norm convergences of states [We6] rather than norm 4 convergence of observables. What is missed in this approach are therefore the operator properties (e) and (f) F) Limit of partition functions. Lie,Sim,LS,WS] This aspect of the classical limit is conceptually straightforward, because it only requires the convergence of some numbers. Of course, it covers only a small fraction of the desirable features listed above. Nevertheless some of the techniques developed for this problem, like upper and lower symbols, or certain operators connecting spin systems of different ....
....means that the half integer labelling the irreducible representation of SU 2 must go to infinity. This limit can be stated exactly along the lines of this paper, with analogous results. It is essentially equivalent to a mean field limit [GW] It can also be carried out for systems of many spins [RW] for more general compact Lie groups [Duf ] and for some quantum groups [GW] For a nonstandard version, see [WW] Acknowledgements This paper has grown out of a series of lectures given at the Marc Kac Seminar in Amsterdam in Summer 1993. The topic of the lectures was non commutative large ....
G.A. Raggio and R.F. Werner: "The Gibbs variational principle for inhomogeneous mean field systems", Helv.Phys.Acta 64 (1991) 633--667
On the free-energy of the Hopfield model - Guerberoff, Raggio (1995) Self-citation (Raggio) (Correct)
....the free energy of the Hopfield model G.R. Guerberoff y , and G.A. Raggio z Facultad de Matem atica, Astronom ia y F isica Universidad Nacional de C ordoba Ciudad Universitaria, 5000 C ordoba, Argentina September 1995 Abstract The general theory of inhomogeneous mean field systems of Ref. [18] provides a variational expression for the (almost sure) limiting free energy density of the Hopfield model H fg N;p (S) Gamma 1 2N N X i;j=1 p X =1 i j S i S j for Ising spins S i and p random patterns = 1 ; 2 ; Delta Delta Delta ; N ) under the assumption ....
....expectation) converge as h Sigma0 weakly and almost surely to the point measure sitting at a Sigma (fi) times the th unit vector in IR N . 2 The purpose of this note is, firstly, to point out an alternative treatment of the case of finitely many patterns using the methods of Refs. [17, 18]. These papers provide a general and efficent treatment of the equilibrium thermodynamics of arbitrary mean field systems. The last section of the second paper [18] gives a general result which can be applied directly to the case of finite p. Moreover, these results are obtained under an ergodic ....
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G.A. Raggio, and R.F. Werner, The Gibbs variational principle for inhomogeneous mean-field systems, Helvet. Phys. Acta 64, 633-667 (1991).
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