PMN: a minimal induced-moment soft pseudo-spin glass perspective

An argument that relaxor ferroelectricity in the isovalent alloy $\mathrm {Ba(Zr}_{1-x}\mathrm{Ti}_{x})\mathrm{O}_3$ can be understood as an induced moment soft pseudo-spin glass on the B-ions of the $\mathrm{ABO}_{3}$ matrix is extended to the experimentally paradigmic but theoretically more complex heterovalent relaxor $\mathrm {Pb(Mg}_{1/3}\mathrm{Nb}_{2/3}\mathrm{)O}_3$ (PMN). It is argued that interesting behaviour of the onset of non-ergodicity, frequency-dependent susceptibility peaks and precursor nanodomains can be understood from analagous considerations of the B-ions, with the displacements of the Pb ions a largely independent, but distracting, side-feature. This contrasts with conventional conceptualizations

Correlated adaptation of agents in a simple market: a statistical physics perspective

We discuss recent work in the study of a simple model for the collective behaviour of diverse speculative agents in an idealized stockmarket, considered from the perspective of the statistical physics of many-body systems. The only information about other agents available to any one is the total trade at time steps. Evidence is presented for correlated adaptation and phase transitions/crossovers in the global volatility of the system as a function of appropriate information scaling dimension. Stochastically controlled irrationally of individual agents is shown to be globally advantageous. We describe the derivation of the underlying effective stochastic differential equations which govern the dynamics, and make an interpretation of the results from the point of view of the statistical physics of disordered systems.Comment: 15 Pages. 5 figure

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

Stability of solutions of the Sherrington-Kirkpatrick model with respect to replications of the phase space

We use real replicas within the Thouless, Anderson and Palmer construction to investigate stability of solutions with respect to uniform scalings in the phase space of the Sherrington-Kirkpatrick model. We show that the demand of homogeneity of thermodynamic potentials leads in a natural way to a thermodynamically dependent ultrametric hierarchy of order parameters. The derived hierarchical mean-field equations appear equivalent to the discrete Parisi RSB scheme. The number of hierarchical levels in the construction is fixed by the global thermodynamic homogeneity expressed as generalized de Almeida Thouless conditions. A physical interpretation of a hierarchical structure of the order parameters is gained.Comment: REVTeX4, 22 pages, second extended version to be published in Phys. Rev.