We study a multi-species spin glass system where the density of each species is kept fixed at increasing volumes. The model reduces to the Sherrington-Kirkpatrick one for the single species case. The existence of the thermodynamic limit is proved for all densities values under a convexity condition on the interaction. The thermodynamic properties of the model are investigated and the annealed, the replica symmetric and the replica symmetry breaking bounds are proved using Guerra's scheme. The annealed approximation is proved to be exact under a high temperature condition. We show that the replica symmetric solution has negative entropy at low temperatures. We study the properties of a suitably defined replica symmetry breaking solution and we optimise it within a novel ziggurat ansatz. The generalised order parameter is described by a Parisi-like partial differential equation.
A mean-field monomer-dimer model which includes an attractive interaction among both monomers and dimers is introduced and its exact solution rigorously derived.
The number of monomers, in a monomer-dimer mean-field model with an attractive potential, fluctuates according to the central limit theorem when the parameters are outside the critical curve. At the critical point the model belongs to the same universality class of the mean-field ferromagnet. Along the critical curve the monomer and dimer phases coexist.
In this paper we study the equilibrium statistical mechanical as well as the dynamical properties of a Sherrington and Kirkpatrick model in a multi-bath setting introduced in [4]. We show that the free energy per particle in the thermodynamical limit obeys a variational principle of Parisi type.The relation between the resulting order parameters is discussed.To Giorgio Parisi on his 70-th birthdaywhere Z J = σ e −βH(σ) is the partition function given J, a random variable depending on the disorder J obtained integrating on the spins. By definition we have that P (0) corresponds to the quenched equilibrium while P (1) to the annealed one. Hence ζ can be viewed as a scale parameter in the unit interval interpolating between the quenched case with annealed one [2]. The origins of (1) are to be found on the replica approach to spin glasses [14] where ζ is at the outset an integer. Almost thirty years ago Kondor [12] calculated (1) using the replica trick for the partition function of the Sherrington arXiv:1903.01892v1 [cond-mat.dis-nn]
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