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Disordered Statistical Mechanics and Applications

The research topics of this group are centered around the statistical mechanics of disordered systems of which the spin glass is a prototype. Since the spectacular success of the replica-symmetry-breaking Parisi theory for the mean field spin glass model the problem of deriving it on rigorous mathematical grounds has involved mathematicians and mathematical physicists.

In recent times the group has extended the methods of the quenched measure also to monomer-dimers systems outside for the purely repulsive interaction and beyond.

The group is also active on the applications of statistical mechanics methods to the descritpion of complex systems, especially those emerging in the socio-economic sciences.

Keywords of the research group activity are: thermodynamic limit, phase transitions, critical point, ultrametricity, violation of the central limit laws, inverse problems in statistical mechanics, correlation inequalities.

Group members

Pierluigi Contucci

Emanuele Mingione

Francesca Collet

Sander Dommers

Diego Alberici (PhD Student)

Research Partners

Alina Sirbu, University of Bologna (Italy),

Cecilia Vernia, University of Modena (Italy),

Claudio Giberti, University of Modena (Italy),

Cristian Giardina, University of Modena (Italy),

Francesco Unguendoli, University of Modena (Italy),

Daniele Tantari, Scuola Normale Superiore (Italy),

Adriano Barra, University of Roma La Sapienza (Italy),

Elena Agliari, University of Roma La Sapienza (Italy),

Giorgio Parisi, University of Roma La Sapienza (Italy),

Federico Ricci Tersenghi, University of Roma La Sapienza (Italy),

Raffaella Burioni, University of Parma (Italy),

Joel Lebowitz, Rutgers University (USA),

Micael Aizenman, Princeton University (USA),

Shannon Starr, University of Birmingham (USA),

Hidetoshi Nishimori, Tokyo Institute of Technology (Japan),

Rickard Sandell, University Carlos III Madrid (Spain),