17 research outputs found
Role of the Tracy-Widom distribution in the finite-size fluctuations of the critical temperature of the Sherrington-Kirkpatrick spin glass
We investigate the finite-size fluctuations due to quenched disorder of the
critical temperature of the Sherrington-Kirkpatrick spin glass. In order to
accomplish this task, we perform a finite-size analysis of the spectrum of the
susceptibility matrix obtained via the Plefka expansion. By exploiting results
from random matrix theory, we obtain that the fluctuations of the critical
temperature are described by the Tracy-Widom distribution with a non-trivial
scaling exponent 2/3
Numerical simulations of liquids with amorphous boundary conditions
It has recently become clear that simulations under amorphpous boundary
conditions (ABCs) can provide valuable information on the dynamics and
thermodynamics of disordered systems with no obvious ordered parameter. In
particular, they allow to detect a correlation length that is not measurable
with standard correlation functions. Here we explain what exactly is meant by
ABCs, discuss their relation with point-to-set correlations and briefly
describe some recent results obtained with this technique.Comment: Presented at STATPHYS 2
Finite-size scaling analysis of the distributions of pseudo-critical temperatures in spin glasses
Using the results of large scale numerical simulations we study the
probability distribution of the pseudo critical temperature for the
three-dimensional Edwards-Anderson Ising spin glass and for the fully connected
Sherrington-Kirkpatrick model. We find that the behavior of our data is nicely
described by straightforward finite-size scaling relations.Comment: 23 pages, 9 figures. Version accepted for publication in J. Stat.
Mec