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Publication

The Multi-species Mean-Field Spin-Glass on the Nishimori Line

Emanuele Mingione, Diego Alberici
2021
Journal Articles

Résumé

In this paper we study a multi-species disordered model on the Nishimori line. The typical properties of this line, a set of identities and inequalities among correlation functions, allow us to prove the replica symmetry i.e. the concentration of the order parameter. When the interaction structure is elliptic we rigorously compute the exact solution of the model in terms of a finite-dimensional variational principle and we study its properties.

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https://infoscience.epfl.ch/entities/publication/49eb86fb-1cfe-4d38-98f3-0cd8ebb36f2c

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Emanuele Mingione, Diego Alberici
2021
Journal Articles

Résumé

Source officielle

https://infoscience.epfl.ch/entities/publication/49eb86fb-1cfe-4d38-98f3-0cd8ebb36f2c

À propos de ce résultat

Concepts associés (19)

Exact solutions in general relativity

In general relativity, an exact solution is a solution of the Einstein field equations whose derivation does not invoke simplifying assumptions, though the starting point for that derivation may be an idealized case like a perfectly spherical shape of matter. Mathematically, finding an exact solution means finding a Lorentzian manifold equipped with tensor fields modeling states of ordinary matter, such as a fluid, or classical non-gravitational fields such as the electromagnetic field.

Fluid solution

In general relativity, a fluid solution is an exact solution of the Einstein field equation in which the gravitational field is produced entirely by the mass, momentum, and stress density of a fluid. In astrophysics, fluid solutions are often employed as stellar models. (It might help to think of a perfect gas as a special case of a perfect fluid.) In cosmology, fluid solutions are often used as cosmological models.

Dust solution

In general relativity, a dust solution is a fluid solution, a type of exact solution of the Einstein field equation, in which the gravitational field is produced entirely by the mass, momentum, and stress density of a perfect fluid that has positive mass density but vanishing pressure. Dust solutions are an important special case of fluid solutions in general relativity. A pressureless perfect fluid can be interpreted as a model of a configuration of dust particles that locally move in concert and interact with each other only gravitationally, from which the name is derived.

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