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 $B$ (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