Geometric and algebraic structures of complex systems in statistical physics
The aim of the project is twofold.
The first purpose is to complete the development of a novel approach to the study of geometric and algebraic structures arising in the statistical description of macroscopic systems. Novel concepts of singular sectors of partition functions, statistical amoebas and hypersurfaces allow to understand several important features of statistical systems hardly treatable by standard techniques.
The second goal is to apply this formalism to investigate a class of statistical systems of current interest, including spin glasses, spin ices, general frustrated and metastable macroscopic systems. The approach is expected to provide an efficient tool for studying important features of such systems, in particular, structure of phase transitions of different kinds, residual entropy, types of equilibrium, associated networks and the comparison with recent experimental data.
This job comes from a partnership with Science Magazine and