Related papers: Free energy upper bound for mean-field vector spin…
Inspired by a continuously increasing interest in modeling and framing complex systems in a thermody- namic rationale, in this paper we continue our investigation in adapting well known techniques (originally stemmed in fields of physics…
Universal bounds for the potential energy of weighted spherical codes are obtained by linear programming. The universality is in the sense of Cohn-Kumar -- every attaining code is optimal with respect to a large class of potential functions…
We focus on spherical spin glasses whose Parisi distribution has support of the form $[0,q]$. For such models we construct paths from the origin to the sphere which consistently remain close to the ground-state energy on the sphere of…
The surface free energy is the difference between the free energies for a system with open boundary conditions and the same system with periodic boundary conditions. We use the quantum transfer matrix formalism to express the surface free…
We show that the limiting free energy in Sherrington-Kirkpatrick's Spin Glass Model does not depend on the environment.
We develop a generalized TAP approach for the multi-species version of the spherical mixed $p$-spin models. In particular, we prove a generalized TAP representation for the free energy at any overlap vector which is multi-samplable in an…
The free energy of TAP-solutions for the SK-model of mean field spin glasses can be expressed as a nonlinear functional of local terms: we exploit this feature in order to contrive abstract REM-like models which we then solve by a classical…
We calculate the naive defect energy $\Delta E$ of Ising spin glass(SG) models in two dimensions using conjugate boundary conditions. We predict that, in the $\pm J$ model, the averaged value $\bar{\Delta E}$ converges to some non-zero…
We consider identical copies of spin glasses in finite dimension coupled at the boundaries. This allows to identify the spin glass analogous of twisted boundary conditions in ferromagnetic system and leads to the definition of an interface…
We propose a simpler approach to identifying the limit of free energy in a vector spin glass model by adding a self-overlap correction to the Hamiltonian. This avoids constraining the self-overlap and allows us to identify the limit with…
A comprehensive review will be given about the rich mathematical structure of mean field spin glass theory, mostly developed, until now, in the frame of the methods of theoretical physics, based on deep physical intuition and hints coming…
We study spin glasses with Kac type interaction potential for small but finite inverse interaction range $\gamma$. Using the theoretical setup of coupled replicas, through the replica method we argue that the probability of overlap profiles…
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…
Free energy as a function of temperature and the bubble radius is determined for spherical bubbles created in cosmological first order phase transitions. The phase transition is assumed to be driven by an order parameter (e.g. a Higgs…
We consider the Hamiltonians of mean-field spin glasses, which are certain random functions $H_N$ defined on high-dimensional cubes or spheres in $\mathbb R^N$. The asymptotic maximum values of these functions were famously obtained by…
The scaling properties of the soft-sphere potential allow the derivation of an exact expression for the pressure of a frozen liquid, i.e., the pressure corresponding to configurations which are local minima in its multidimensional potential…
We examined energy spectrums of some particular systems of binary spins. It is shown that the configuration space can be divided into classes, and in the limit the energy distributions in these classes can be approximated by the normal…
By using a simple interpolation argument, in previous work we have proven the existence of the thermodynamic limit, for mean field disordered models, including the Sherrington-Kirkpatrick model, and the Derrida p-spin model. Here we extend…
In this note, we consider the multi-species Sherrington-Kirkpatrick spin glass model at its conjectured critical temperature, and we show that, when the variance profile matrix $\Delta^2$ is positive semi-definite, the variance of the free…
The static free energy of glassy systems can be expressed in terms of the Parisi order parameter function. When this function has a discontinuity, the location of the step is determined by maximizing the free energy. In dynamics a…