Invited Speaker - Enzo Olivieri (Roma "Tor Vergata")

Title:

Random perturbations of strong mixing lattice spin systems: beating Griffith singularity up to criticality

Abstract:

In a series of papers in collaboration with Lorenzo Bertini and Emilio Cirillo we proposed a unified approach to two (apparently very different) problems:
1) Weak Gibbs property for measures arising by the application of renormalization group (RG) maps together with the convergence of the iterates of these maps and
2) the Griffith phase (Cinfinity but non-analytic thermodynamic functions) for desordered systems.
The new feature of our approach is that it is valid even close to criticality (the only really interesting case).
To study this two kind of systems we use a "graded" cluster expansion whose minimal scale-length diverges when the thermodynamic parameters tend to the values corresponding to the critical point of the original system.

References:

[1] Bertini, Lorenzo; Cirillo, Emilio N. M.; Olivieri, Enzo Graded cluster expansion for lattice systems. Comm. Math. Phys. 258 (2005), no. 2, 405--443
[2] Bertini, Lorenzo; Cirillo, Emilio N. M.; Olivieri, Enzo Renormalization group in the uniqueness region: weak Gibbsianity and convergence. Commun. Math. Phys. 261, No. 2, 323-378 (2006)
[3] Bertini, Lorenzo; Cirillo, Emilio N. M.; Olivieri, Enzo Perturbative Analysis of Disordered Ising Models Close to Criticality Journal of Statistical Physics Volume 126, (2007), 987-1006,
[4] Bertini, Lorenzo; Cirillo, Emilio N. M.; Olivieri, Enzo Random perturbations of strong mixing lattice spin systems (in preparation)