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

Absence of Replica Symmetry Breaking in a Region of the Phase Diagram of the Ising Spin Glass

We prove that the distribution functions of magnetization and spin glass order parameter coincide on the Nishimori line in the phase diagram of the $\pm J$ Ising model in any dimension. This implies absence of replica symmetry breaking because the distribution function of magnetization consists only of two delta functions, suggesting the same simple structure for the distribution of spin glass order parameter. It then follows that the mixed (glassy) phase, where the ferromagnetic order coexists with complex phase space, should lie, if any, below the Nishimori line. We also argue that the AT line to mark the onset of RSB with a continous distribution of the spin glass order parameter, if any again, would start with an infinite slope from the multicritical point where paramagnetic, ferromagnetic and spin glass phases merge.Comment: 6 pages, 3 figures, uses aipproc.st

Comment on `Replica analysis of the p-spin interaction Ising spin-glass model'

We demonstrate that the analytic calculation of the 1RSB break point parameter in a paper by de Oliveira and Fontanari[1] is erroneous, due to the omission of a higher order term in a lengthy perturbative calculation, and provide a refinement of the accompanying numerical results. [1] V. M. de Oliveira and J. F. Fontanari, J. Phys. A 32, 2285 (1998)Comment: 4 pages, AMS LaTeX, 1 EPS figure; minor typo correcte