1202.4168 (Ulisse Ferrari et al.)

On the two-steps relaxation of mean-field glasses: p-spin model    [PDF]

Ulisse Ferrari, Luca Leuzzi, Giorgio Parisi, Tommaso Rizzo

Critical slowing down dynamics of supercooled glass-forming liquids is
usually understood at the mean-field level in the framework of Mode Coupling
Theory, providing a two-time relaxation scenario and power-law behaviors of the
time correlation function at dynamic criticality. In this work we derive
critical slowing down exponents of spin-glass models undergoing discontinuous
transitions by computing their Gibbs free energy and connecting the dynamic
behavior to static "in-state" properties. Both the spherical and Ising versions
are considered and, in the simpler spherical case, a generalization to
arbitrary schematic Mode Coupling kernels is presented. Comparison with dynamic
results available in literature is performed. Analytical predictions for the
Ising case are provided for any $p$.

View original: http://arxiv.org/abs/1202.4168