arXiv subjects

Alain Billoire

Publications and source records attributed to Alain Billoire.

23 records · Page 2Linked to original sources

arXiv2001

About the Functional Form of the Parisi Overlap Distribution for the Three-Dimensional Edwards-Anderson Ising Spin Glass

Recently, it has been conjectured that the statistics of extremes is of relevance for a large class of correlated system. For certain probability densities this predicts the characteristic large $x$ fall-off behavior $f(x)\sim\exp (-a e^x)$, $a>0$. Using a multicanonical Monte Carlo technique, we have calculated the Parisi overlap distribution $P(q)$ for the three-dimensional Edward-Anderson Ising spin glass at and below the critical temperature, even where $P(q)$ is exponentially small. We find that a probability distribution related to extreme order statistics gives an excellent description of $P(q)$ over about 80 orders of magnitude.

cond-mat.stat-mech↗

arXiv2001

Correlation Time Scales in the Sherrington-Kirkpatrick Model

We investigate the dynamical behavior of the Sherrington-Kirkpatrick mean field model of spin glasses by numerical simulation. All the time scales tau we have measured behave like ln(tau) propto N^epsilon, where N is the number of spins and epsilon \simeq 1/3. This is true whether the autocorrelation function used to define tau is sensitive to the full reversal of the system or not.

cond-mat.stat-mech↗

arXiv2000

Spin glass overlap barriers in three and four dimensions

For the Edwards-Anderson Ising spin-glass model in three and four dimensions (3d and 4d) we have performed high statistics Monte Carlo calculations of those free-energy barriers $F^q_B$ which are visible in the probability density $P_J(q)$ of the Parisi overlap parameter $q$. The calculations rely on the recently introduced multi-overlap algorithm. In both dimensions, within the limits of lattice sizes investigated, these barriers are found to be non-self-averaging and the same is true for the autocorrelation times of our algorithm. Further, we present evidence that barriers hidden in $q$ dominate the canonical autocorrelation times.

cond-mat.dis-nn↗

arXiv1998

Energy barriers of spin glasses from multi-overlap simulations

We report large-scale simulations of the three-dimensional Edwards-Anderson Ising spin glass system using the recently introduced multi-overlap Monte Carlo algorithm. In this approach the temperature is fixed and two replica are coupled through a weight factor such that a broad distribution of the Parisi overlap parameter $q$ is achieved. Canonical expectation values for the entire $q$-range (multi-overlap) follow by reweighting. We present an analysis of the performance of the algorithm and in particular discuss results on spin glass free-energy barriers which are hard to obtain with conventional algorithms. In addition we discuss the non-trivial scaling behavior of the canonical $q$-distributions in the broken phase.

cond-mat.dis-nn↗

arXiv1992

Numerical Study of Finite Size Scaling for First Order Phase Transitions

I present results of simulations of the q=10 and q=20 2-d Potts models in the transition region. The asymptotic finite size behavior sets in only for extremely large lattices. We learn from this simulation that finite size scaling cannot be used to decide that a transition is first order.

hep-lat↗