200 research outputs found
On temperature chaos in Ising and XY Spin Glasses
We argue that the chaotic temperature effect predicted in Ising spin glasses
should be stronger when one considers continuous (XY, Heisenberg) kind of
spins, due to bigger entropic fluctuations. We then discuss the behavior of 3d
spin glasses using the Migdal-Kadanoff Renormalization Group for Ising and XY
spins, where we show explicitly that the chaotic length scale, the length
beyond which equilibrium configurations are completly reshuffled when one
changes temperature, could be far smaller for XY than for Ising spins. These
results could thus explain why experiments are seeing a stronger rejuvenation
effect for continuous spins.Comment: 7 pages, 6 figures, accepted for publicatio
How many colors to color a random graph? Cavity, Complexity, Stability and all that
We review recent progress on the statiscal physics study of the problem of
coloring random graphs with q colors. We discuss the existence of a threeshold
at connectivity c_q=2q log q-log q-1+o(1) separting two phases which are
respectivily COL(orable) and UNCOL(orable) with q colors; We also argue that
the so-called one-step replica symmetry breaking ansatz used to derive these
results give it exact threshold values, and draw a general phase diagram of the
problem.Comment: 4 pages, 2 figures, proceeding of "Statistical Physics of Disordered
Systems and Its Applications", Hayama (Japan), July 200
Replica Analysis and Approximate Message Passing Decoder for Superposition Codes
Superposition codes are efficient for the Additive White Gaussian Noise
channel. We provide here a replica analysis of the performances of these codes
for large signals. We also consider a Bayesian Approximate Message Passing
decoder based on a belief-propagation approach, and discuss its performance
using the density evolution technic. Our main findings are 1) for the sizes we
can access, the message-passing decoder outperforms other decoders studied in
the literature 2) its performance is limited by a sharp phase transition and 3)
while these codes reach capacity as (a crucial parameter in the code)
increases, the performance of the message passing decoder worsen as the phase
transition goes to lower rates.Comment: 5 pages, 5 figures, To be presented at the 2014 IEEE International
Symposium on Information Theor
Following Gibbs States Adiabatically - The Energy Landscape of Mean Field Glassy Systems
We introduce a generalization of the cavity, or Bethe-Peierls, method that
allows to follow Gibbs states when an external parameter, e.g. the temperature,
is adiabatically changed. This allows to obtain new quantitative results on the
static and dynamic behavior of mean field disordered systems such as models of
glassy and amorphous materials or random constraint satisfaction problems. As a
first application, we discuss the residual energy after a very slow annealing,
the behavior of out-of-equilibrium states, and demonstrate the presence of
temperature chaos in equilibrium. We also explore the energy landscape, and
identify a new transition from an computationally easier canyons-dominated
region to a harder valleys-dominated one.Comment: 6 pages, 7 figure
- …