A note on the Guerra and Talagrand theorems for Mean Field Spin Glasses: the simple case of spherical models

The aim of this paper is to discuss the main ideas of the Talagrand proof of the Parisi Ansatz for the free-energy of Mean Field Spin Glasses with a physicist's approach. We consider the case of the spherical $p$-spin model, which has the following advantages: 1) the Parisi Ansatz takes the simple ``one step replica symmetry breaking form'', 2) the replica free-energy as a function of the order parameters is simple enough to allow for numerical maximization with arbitrary precision. We present the essential ideas of the proof, we stress its connections with the theory of effective potentials for glassy systems, and we reduce the technically more difficult part of the Talagrand's analysis to an explicit evaluation of the solution of a variational problem.Comment: 20 pages, 5 figures. Added references and minor language correction

Spin glass models with Kac interactions

In this paper I will review my work on disordered systems -spin glass model with two body and $p>2$ body interactions- with long but finite interaction range $R$. I will describe the relation of these model with Mean Field Theory in the Kac limit and some attempts to go beyond mean field.Comment: Proceedings of the Stat-phys23 conferenc

Exact Solutions of Bethe-Salpeter Equations with Instantaneous Interactions

The Bethe-Salpeter approach allows for quantum-field-theoretic descriptions of relativistic bound states; its inherent complexity, however, usually prevents to find its exact solutions. Under suitable simplifying assumptions about the systems discussed, we derive analytically some examples of rigorous solutions to the instantaneous homogeneous Bethe-Salpeter equation by relating tentative solutions to the interactions responsible for the formation of bound states.Comment: 16 pages, 3 figures; v2: slightly augmented summary, matches version in PR

Instantaneous Bethe-Salpeter Look at the Lightest Pseudoscalar Mesons

Within our description of Goldstone-type pseudoscalar mesons as almost massless bound states of quark and antiquark by a three-dimensional bound-state equation of Bethe-Salpeter origin, taking into account the pointwise behaviour of the full light-quark propagators enables to characterize the effective interquark interactions more precisely than earlier studies exploiting just specific aspects.Comment: 4 pages, 2 figures, contributed to "XVII International Conference on Hadron Spectroscopy and Structure - Hadron2017" (25 - 29 September 2017, Salamanca, Spain

The Spinless Relativistic Woods-Saxon Problem

Motivated by the observation of a recent renewal of rather strong interest in the description of bound states by (semi-) relativistic equations of motion, we revisit, for the example of the Woods-Saxon interactions, the eigenvalue problem posed by the spinless Salpeter equation and recall various elementary knowledge, considerations, and techniques that practitioners seeking solutions to this specific reduction of the Bethe-Salpeter equation may find helpful.Comment: 12 page