We report a high-precision finite-size scaling study of the critical behavior of the three-dimensional Ising Edwards-Anderson model (the Ising spin glass). We have thermalized lattices up to $L=40$ using the Janus dedicated computer. Our analysis takes into account leading-order corrections to scaling. We obtain ${T}_{\mathrm{c}}=1.1019(29)$ for the critical temperature, $$\nu${}=2.562(42)$ for the thermal exponent, $$\eta${}=$-${}0.3900(36)$ for the anomalous dimension, and $$\omega${}=1.12(10)$ for the exponent of the leading corrections to scaling. Standard (hyper)scaling relations yield $$\alpha${}=$-${}5.69(13)$, $$\beta${}=0.782(10)$, and $$\gamma${}=6.13(11)$. We also compute several universal quantities at ${T}_{\mathrm{c}}$.

We study numerically the nonequilibrium dynamics of the Ising spin glass, for a time spanning 11 orders of magnitude, thus approaching the experimentally relevant scale (i.e., seconds). We introduce novel analysis techniques to compute the coherence length in a model-independent way. We present strong evidence for a replicon correlator and for overlap equivalence. The emerging picture is compatible with noncoarsening behavior.

Janus is a modular, massively parallel, and reconfigurable FPGA-based computing system. Each Janus module has one computational core and one host. Janus is tailored to, but not limited to, the needs of a class of hard scientific applications characterized by regular code structure, unconventional data-manipulation requirements, and a few Megabits database. The authors discuss this configurable system's architecture and focus on its use for Monte Carlo simulations of statistical mechanics, as Janus performs impressively on this class of application.

This paper describes the architecture, the development and the implementation of Janus II, a new generation application-driven number cruncher optimized for Monte Carlo simulations of spin systems (mainly spin glasses). This domain of computational physics is a recognized grand challenge of high-performance computing: the resources necessary to study in detail theoretical models that can make contact with experimental data are by far beyond those available using commodity computer systems. On the other hand, several specific features of the associated algorithms suggest that unconventional computer architectures - that can be implemented with available electronics technologies - may lead to order of magnitude increases in performance, reducing to acceptable values on human scales the time needed to carry out simulation campaigns that would take centuries on commercially available machines. Janus II is one such machine, recently developed and commissioned, that builds upon and improves on the successful JANUS machine, which has been used for physics since 2008 and is still in operation today. This paper describes in detail the motivations behind the project, the computational requirements, the architecture and the implementation of this new machine and compares its expected performances with those of currently available commercial systems. (C) 2013 Elsevier B.V. All rights reserved