Glass transition and random walks on complex energy landscapes

Andrea Baronchelli , Alain Barrat (1, 2, 3, 4) , Romualdo Pastor-Satorras

1 CPT - E5 Physique statistique et systèmes complexes
2 CPT - Centre de Physique Théorique - UMR 6207
3 Complex Networks Lagrange Laboratory
4 CPT - Centre de Physique Théorique - UMR 7332

We present a simple mathematical model of glassy dynamics seen as a random walk in a directed, weighted network of minima taken as a representation of the energy landscape. Our approach gives a broader perspective to previous studies focusing on particular examples of energy landscapes obtained by sampling energy minima and saddles of small systems. We point out how the relation between the energies of the minima and their number of neighbors should be studied in connection with the network's global topology, and show how the tools developed in complex network theory can be put to use in this context.

Domaines: Mécanique statistique [cond-mat.stat-mech]

Andrea Baronchelli, Alain Barrat, Romualdo Pastor-Satorras. Glass transition and random walks on complex energy landscapes. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2009, 80, pp.020102(R). ⟨10.1103/PhysRevE.80.020102⟩. ⟨hal-00380503⟩