Landscape Paradigms in Physics and Biology: Introduction and Overview

A brief introductory overview in general terms is given of concepts, issues and applications of the paradigm of rugged landscapes in the contexts of physics and biology.Comment: 10 pages, to be published in Physica

Spin Glasses: a Perspective

A brief personal perspective is given of issues, questions, formulations, methods, some answers and selected extensions posed by the spin glass problem, showing how considerations of an apparently insignificant and practically unimportant group of metallic alloys stimulated an explosion of new insights and opportunities in the general area of complex many-body systems and still is doing soComment: For publication in the proceedings of International Conference on "Equilibrium and Dynamics of Spin Glasses" (Ascona, Switzerland: April 2004). V2 has minor changes to clarify and correct typo

The Minority Game: a statistical physics perspective

A brief review is given of the minority game, an idealized model stimulated by a market of speculative agents, and its complex many-body behaviour. Particular consideration is given to analytic results for the model rather than discussions of its relevance in real-world situations.Comment: 6 pages, 2 figures. Submitted for publication in the proceedings of the Econophysics Colloquium, Canberra, Australia (November 2005

On exact mappings between fermionic Ising spin glass and classical spin glass models

We present in this paper exact analytical expressions for the thermodynamical properties and Green functions of a certain family of fermionic Ising spin-glass models with Hubbard interaction, by noticing that their Hamiltonian is a function of the number operator only. The thermodynamical properties are mapped to the classical Ghatak-Sherrington spin-glass model while the the Density of States (DoS) is related to its joint spin-field distribution. We discuss the presence of the pseudogap in the DoS with the help of this mapping.Comment: 6 page

Irreducible free energy expansion and overlaps locking in mean field spin glasses

We introduce a diagrammatic formulation for a cavity field expansion around the critical temperature. This approach allows us to obtain a theory for the overlap's fluctuations and, in particular, the linear part of the Ghirlanda-Guerra relationships (GG) (often called Aizenman-Contucci polynomials (AC)) in a very simple way. We show moreover how these constraints are "superimposed" by the symmetry of the model with respect to the restriction required by thermodynamic stability. Within this framework it is possible to expand the free energy in terms of these irreducible overlaps fluctuations and in a form that simply put in evidence how the complexity of the solution is related to the complexity of the entropy.Comment: 19 page

Glassy dynamics in the HMF model

We discuss the glassy dynamics recently found in the meta-equilibrium quasi stationary states (QSS) of the HMF model. The relevance of the initial conditions and the connection with Tsallis nonextensive thermostatistics is also addressed.Comment: 10 pages, 4 figures, Proceedings of the Int. Conference Next2003 21-28 september 2003, Villasimius (CA) Italy, submitted to Physica