Our research group will consider the study of the statistical mechanics properties, especially at equilibrium (but not only) of disordered systems described by quenched measures. They include spin glasses and diluted systems on random graphs (like scale free networks with small world features) which have important applications in socio economic sciences. The group expertises belong to the mathematical physics culture and have strong links with theoretical physics both from the type of problems that we study and from the methodological point of view which include numerical and rigorous results. The models to which our research will be concentrated on are those with the presence of interacting variables with a slow dynamical behavior (coupling variables) and those with quick dynamics like spins. Such systems are well described by quenched free energies and correlation functions averaged on the disorder. The investigation of the rigorous properties both on the mean field models and on the finite dimensional models is at the heart of the project. Among them the one who is commonly called "ultrametricity" has been, for more than three decades, resisting the attempts of a rigorous deduction from physical principles even in the mean field case and is considered a key issue in the finite dimensional case. Our work will be focused also on diluted models, especially of mean field nature, since they are the closest to the socio economic application that we work on. Concerning those applications that statistical mechanics has been involved with for more than a decade our central topic will be the solution of the inverse problem. In fact, while statistical mechanics derives free energy and correlation functions in its standard use, the inverse problem consist in deducing the interaction coefficients starting from the knowledge of correlation functions statistical data. In this perspective part of the work will be to deduce the analytical properties of the models who lead to inversion formulas and part will be devoted to the statistical evaluation of the correlations in those cases in which the phase space is well known.
Pierluigi Contucci (2013). Statistical Mechanics of Disordered and Complex Systems.
Statistical Mechanics of Disordered and Complex Systems
CONTUCCI, PIERLUIGI
2013
Abstract
Our research group will consider the study of the statistical mechanics properties, especially at equilibrium (but not only) of disordered systems described by quenched measures. They include spin glasses and diluted systems on random graphs (like scale free networks with small world features) which have important applications in socio economic sciences. The group expertises belong to the mathematical physics culture and have strong links with theoretical physics both from the type of problems that we study and from the methodological point of view which include numerical and rigorous results. The models to which our research will be concentrated on are those with the presence of interacting variables with a slow dynamical behavior (coupling variables) and those with quick dynamics like spins. Such systems are well described by quenched free energies and correlation functions averaged on the disorder. The investigation of the rigorous properties both on the mean field models and on the finite dimensional models is at the heart of the project. Among them the one who is commonly called "ultrametricity" has been, for more than three decades, resisting the attempts of a rigorous deduction from physical principles even in the mean field case and is considered a key issue in the finite dimensional case. Our work will be focused also on diluted models, especially of mean field nature, since they are the closest to the socio economic application that we work on. Concerning those applications that statistical mechanics has been involved with for more than a decade our central topic will be the solution of the inverse problem. In fact, while statistical mechanics derives free energy and correlation functions in its standard use, the inverse problem consist in deducing the interaction coefficients starting from the knowledge of correlation functions statistical data. In this perspective part of the work will be to deduce the analytical properties of the models who lead to inversion formulas and part will be devoted to the statistical evaluation of the correlations in those cases in which the phase space is well known.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
