The Fully Frustrated Hypercubic Model is Glassy and Aging at Large DD

We discuss the behavior of the fully frustrated hypercubic cell in the infinite dimensional mean-field limit. In the Ising case the system undergoes a glass transition, well described by the random orthogonal model. Under the glass temperature aging effects show clearly. In the $XY$ case there is no sign of a phase transition, and the system is always a paramagnet.Comment: Figures added in uufiles format, and epsf include

Numerical simulations on the 4d Heisenberg spin glass

We study the 4d Heisenberg spin glass model with Gaussian nearest-neighbor interactions. We use finite size scaling to analyze the data. We find a behavior consistent with a finite temperature spin glass transition. Our estimates for the critical exponents agree with the results from epsilon-expansion.Comment: 11 pages, LaTeX, preprint ROMA1 n. 105

Reaction rate calculation by parallel path swapping

The efficiency of path sampling simulations can be improved considerably using the approach of path swapping. For this purpose, we have devised a new algorithmic procedure based on the transition interface sampling technique. In the same spirit of parallel tempering, paths between different ensembles are swapped, but the role of temperature is here played by the interface position. We have tested the method on the denaturation transition of DNA using the Peyrard-Bishop-Dauxois model. We find that the new algorithm gives a reduction of the computational cost by a factor 20.Comment: 5 pages, 3 figure

Real space application of the mean-field description of spin glass dynamics

The out of equilibrium dynamics of finite dimensional spin glasses is considered from a point of view going beyond the standard `mean-field theory' versus `droplet picture' debate of the last decades. The main predictions of both theories concerning the spin glass dynamics are discussed. It is shown, in particular, that predictions originating from mean-field ideas concerning the violations of the fluctuation-dissipation theorem apply quantitatively, provided one properly takes into account the role of the spin glass coherence length which plays a central role in the droplet picture. Dynamics in a uniform magnetic field is also briefly discussed.Comment: 4 pages, 4 eps figures. v2: published versio

On the Effects of a Bulk Perturbation on the Ground State of 3D Ising Spin Glasses

We compute and analyze couples of ground states of 3D spin glasses before and after applying a volume perturbation which adds to the Hamiltonian a repulsion from the true ground state. The physical picture based on Replica Symmetry Breaking is in excellent agreement with the observed behavior.Comment: 4 pages including 5 .ps figure

Finding long cycles in graphs

We analyze the problem of discovering long cycles inside a graph. We propose and test two algorithms for this task. The first one is based on recent advances in statistical mechanics and relies on a message passing procedure. The second follows a more standard Monte Carlo Markov Chain strategy. Special attention is devoted to Hamiltonian cycles of (non-regular) random graphs of minimal connectivity equal to three

4D Spin Glasses in Magnetic Field Have a Mean Field like Phase

By using numerical simulations we show that the 4D $J=\pm 1$ Edwards Anderson spin glass in magnetic field undergoes a mean field like phase transition. We use a dynamical approach: we simulate large lattices (of volume $V$) and work out the behavior of the system in limit where both $t$ and $V$ go to infinity, but where the limit $V \to \infty$ is taken first. By showing that the dynamic overlap $q$ converges to a value smaller than the static one we exhibit replica symmetry breaking. The critical exponents are compatible with the ones obtained by mean field computations.Comment: Physrev format, 5 ps figures include

3D Spin Glass and 2D Ferromagnetic XY Model: a Comparison

We compare the probability distributions and Binder cumulants of the overlap in the 3D Ising spin glass with those of the magnetization in the ferromagnetic 2D XY model. We analyze similarities and differences. Evidence for the existence of a phase transition in the spin glass model is obtained thanks to the crossing of the Binder cumulant. We show that the behavior of the XY model is fully compatible with the Kosterlitz-Thouless scenario. Finite size effects have to be dealt with by using great care in order to discern among two very different physical pictures that can look very similar if analyzed without large attention.Comment: 14 pages and 6 figures. Also available at http://chimera.roma1.infn.it/index_papers_complex.htm

Sample-to-sample fluctuations of power spectrum of a random motion in a periodic Sinai model

The Sinai model of a tracer diffusing in a quenched Brownian potential is a much studied problem exhibiting a logarithmically slow anomalous diffusion due to the growth of energy barriers with the system size. However, if the potential is random but periodic, the regime of anomalous diffusion crosses over to one of normal diffusion once a tracer has diffused over a few periods of the system. Here we consider a system in which the potential is given by a Brownian Bridge on a finite interval $(0,L)$ and then periodically repeated over the whole real line, and study the power spectrum $S(f)$ of the diffusive process $x(t)$ in such a potential. We show that for most of realizations of $x(t)$ in a given realization of the potential, the low-frequency behavior is $S(f) \sim {\cal A}/f^2$, i.e., the same as for standard Brownian motion, and the amplitude ${\cal A}$ is a disorder-dependent random variable with a finite support. Focusing on the statistical properties of this random variable, we determine the moments of ${\cal A}$ of arbitrary, negative or positive order $k$, and demonstrate that they exhibit a multi-fractal dependence on $k$, and a rather unusual dependence on the temperature and on the periodicity $L$, which are supported by atypical realizations of the periodic disorder. We finally show that the distribution of ${\cal A}$ has a log-normal left tail, and exhibits an essential singularity close to the right edge of the support, which is related to the Lifshitz singularity. Our findings are based both on analytic results and on extensive numerical simulations of the process $x(t)$.Comment: 8 pages, 5 figure

A Non-Disordered Glassy Model with a Tunable Interaction Range

We introduce a non-disordered lattice spin model, based on the principle of minimizing spin-spin correlations up to a (tunable) distance R. The model can be defined in any spatial dimension D, but already for D=1 and small values of R (e.g. R=5) the model shows the properties of a glassy system: deep and well separated energy minima, very slow relaxation dynamics, aging and non-trivial fluctuation-dissipation ratio.Comment: 4 pages, 5 figure