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Annalen der Physik

Energy barriers of spin glasses from multi‐overlap simulations

Wolfhard Janke E, Bernd A. Berg, Alain H. Billoire

Published Nov 1, 1998• 1 citation
Publisher

Abstract

Abstract 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.

DOI
10.1002/andp.199851005-625

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Abstract 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.
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.
We introduce a novel method for numerical spin glass investigations: Simulations of two replica at fixed temperature, weighted to achieve a broad distribution of the Parisi overlap parameter qqq (multioverlap). We demonstrate the feasibility of the approach by studying the 3D Edwards-Anderson Ising ( ${J}_{\mathrm{ik}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ifmmode\pm\else\textpm\fi{}1$) spin glass in the broken phase ( $\ensuremath{\beta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$). This makes it possible to obtain reliable results about spin glass tunneling barriers. In addition, our results indicate a nontrivial scaling behavior of the canonical qqq distributions not only at the freezing point but also deep in the broken phase.
We present results of recent high-statistics Monte Carlo simulations of the Edwards-Anderson Ising spin-glass model in three and four dimensions. The study is based on a non-Boltzmann sampling technique, the multi-overlap algorithm which is specifically tailored for sampling rare-event states. We thus concentrate on those properties which are difficult to obtain with standard canonical Boltzmann sampling such as the free-energy barriers F^q_B in the probability density P_J(q) of the Parisi overlap parameter q and the behaviour of the tails of the disorder averaged density P(q) = [P_J(q)]_av.
For the Edwards-Anderson Ising spin-glass model in three and four dimensions (3d(3d(3d and 4d)4d)4d) we have performed high statistics Monte Carlo calculations of those free-energy barriers FBq{F}_{B}^{q}FBq​ which are visible in the probability density PJ(q){P}_{\mathcal{J}}(q)PJ​(q) of the Parisi overlap parameter q. The calculations rely on the recently introduced multioverlap 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.