Related papers: Constructive Cavity Method
We extend two rigorous results of Aizenman, Lebowitz, and Ruelle in their pioneering paper of 1987 on the Sherrington-Kirkpatrick spin-glass model without external magnetic field to the quantum case with a "transverse field" of strength…
The expression of the free energy density of a classical crystalline system as a gradient expansion in terms of a set of order parameters is developed using classical density functional theory. The goal here is to extend and complete an…
We consider the statistical mechanics of a classical particle in a one-dimensional box subjected to a random potential which constitutes a Wiener process on the coordinate axis. The distribution of the free energy and all correlation…
The sample-to-sample fluctuations Delta F_N of the free energy in the Sherrington-Kirkpatrick model are shown rigorously to be related to bond chaos. Via this connection, the fluctuations become analytically accessible by replica methods.…
Quantum superposition, a cornerstone of quantum mechanics, enables systems to exist in multiple states simultaneously, giving rise to probabilistic outcomes. In quantum information science, conditional entropy has become a key metric for…
The free energy of the chiral Potts model has been obtained in two ways. The first used only the star-triangle relation, symmetries and invariances, and led to a system of equations that implicitly define the free energy, and from which the…
Recently we introduced a new technique for computing the average free energy of a system with quenched randomness. The basic tool of this technique is a distributional zeta-function. The distributional zeta-function is a complex function…
Social free energy has been recently introduced as a measure of social action obtainable in a given social system, without changes in its structure. The authors of this paper argue that social free energy surpasses the gap between the…
The ideas of thermodynamics have proved fruitful in the setting of quantum information theory, in particular the notion that when the allowed transformations of a system are restricted, certain states of the system become useful resources…
We show that classical density functional theory can be based on the constrained search method [M. Levy, Proc. Natl. Acad. Sci. 76, 6062 (1979)]. From the Gibbs inequality one first derives a variational principle for the grand potential as…
In this paper we present a new mathematical rigorous technique for computing the average free energy of a disordered system with quenched randomness, using the replicas. The basic tool of this technique is a distributional zeta-function, a…
A functional representation of free L\'evy processes is established via an ensemble of unitarily invariant Hermitian matrix-valued L\'evy processes. This is accomplished by proving functional asymptotics of their empirical spectral…
An effective method based on Hubbard-Schofield approach [Phys. Lett. A {\bf 40}, 245 (1972)] is developed to calculate the free energy of classical Coulomb systems. This method significantly simplifies the derivation of the cluster…
Estimating the free energy in molecular simulation requires, implicitly or explicitly, counting how many times the system is observed in a finite region. If the simulation is biased by an external potential, the weight of the configurations…
We compute the free energy at all temperatures for the spherical pure $p$-spin models from the generalized Thouless-Anderson-Palmer representation. This is the first example of a mixed $p$-spin model for which the free energy is computed in…
Semiclassical theories like the Thomas-Fermi and Wigner-Kirkwood methods give a good description of the smooth average part of the total energy of a Fermi gas in some external potential when the chemical potential is varied. However, in…
We have substantially extended the high-temperature and low-magnetic-field (and the related low-temperature and high-magnetic-field) bivariate expansions of the free energy for the conventional three-dimensional Ising model and for a…
We consider a spherical spin system with pure 2-spin spherical Sherrington-Kirkpatrick Hamiltonian with ferromagnetic Curie-Weiss interaction. The system shows a two-dimensional phase transition with respect to the temperature and the…
A variational model of pressure-dependent plasticity employing a time-incremental setting is introduced. A novel formulation of the dissipation potential allows one to construct the condensed energy in a variationally consistent manner. For…
We investigate both free energy and complexity of the spherical bipartite spin glass model. We first prove a variational formula in high temperature for the limiting free energy based on the well-known Crisanti-Sommers representation of the…