P. Tellez

Critical behavior of the three-dimensional Ising spin glass

We have simulated, using parallel tempering, the three-dimensional Ising spin glass model with binary couplings in a helicoidal geometry. The largest lattice

Ianus: an adaptive FPGA computer

(L=20)

SUE: A special purpose computer for spin glass models

has been studied using a dedicated computer (the SUE machine). We have obtained, measuring the correlation length in the critical region, strong evidence for a second-order finite-temperature phase transition, ruling out other possible scenarios like a Kosterlitz-Thouless phase transition. Precise values for the \ensuremath{\nu} and \ensuremath{\eta} critical exponents are also presented.

Thermodynamic glass transition in a spin glass without time-reversal symmetry

With Ianus, a next-generation field-programmable gate array (FPGA)-based machine, the authors hope to build a system that can fully exploit the performance potential of FPGA devices. A software platform that simplifies Ianus programming will extend its intended application range to a wide class of interesting and computationally demanding problems.

Reconfigurable computing for Monte Carlo simulations: results and prospects of the Janus project

The use of last generation Programmable Electronic Components makes possible the construction of very powerful and competitive special purpose computers. We have designed, constructed and tested a three-dimensional Spin Glass model dedicated machine, which consists of 12 identical boards. Each single board can simulate 8 different systems, updating all the systems at every clock cycle. The update speed of the whole machine is 217 ps/spin with 48 MHz clock frequency. A device devoted to fast random number generation has been developed and included in every board. The on-board reprogrammability permits us to change easily the lattice size, or even the update algorithm or the action. We present here a detailed description of the machine and the first runs using the Heat Bath algorithm.

The U(1)-Higgs model: critical behaviour in the confining-Higgs region

Spin glasses are a longstanding model for the sluggish dynamics that appear at the glass transition. However, spin glasses differ from structural glasses in a crucial feature: they enjoy a time reversal symmetry. This symmetry can be broken by applying an external magnetic field, but embarrassingly little is known about the critical behavior of a spin glass in a field. In this context, the space dimension is crucial. Simulations are easier to interpret in a large number of dimensions, but one must work below the upper critical dimension (i.e., in d < 6) in order for results to have relevance for experiments. Here we show conclusive evidence for the presence of a phase transition in a four-dimensional spin glass in a field. Two ingredients were crucial for this achievement: massive numerical simulations were carried out on the Janus special-purpose computer, and a new and powerful finite-size scaling method.

Instanton-like contributions to the dynamics of Yang-Mills fields on the twisted torus

We describe Janus, a massively parallel FPGA-based computer optimized for the simulation of spin glasses, theoretical models for the behavior of glassy materials. FPGAs (as compared to GPUs or many-core processors) provide a complementary approach to massively parallel computing. In particular, our model problem is formulated in terms of binary variables, and floating-point operations can be (almost) completely avoided. The FPGA architecture allows us to run many independent threads with almost no latencies in memory access, thus updating up to 1024 spins per cycle. We describe Janus in detail and we summarize the physics results obtained in four years of operation of this machine; we discuss two types of physics applications: long simulations on very large systems (which try to mimic and provide understanding about the experimental non-equilibrium dynamics), and low-temperature equilibrium simulations using an artificial parallel tempering dynamics. The time scale of our non-equilibrium simulations spans eleven orders of magnitude (from picoseconds to a tenth of a second). On the other hand, our equilibrium simulations are unprecedented both because of the low temperatures reached and for the large systems that we have brought to equilibrium. A finite-time scaling ansatz emerges from the detailed comparison of the two sets of simulations. Janus has made it possible to perform spin-glass simulations that would take several decades on more conventional architectures. The paper ends with an assessment of the potential of possible future versions of the Janus architecture, based on state-of-the-art technology.

The confining-Higgs phase transition in U(1)-Higgs LGT

Abstract We study numerically the critical properties of the U(1)-Higgs lattice model, with fixed Higgs modulus, in the region of small gauge coupling where the Higgs and confining phases merge. We find evidence for a first-order transition line that ends in a second-order point. By means of a rotation in parameter space we introduce thermodynamic magnitudes and critical exponents in close resemblance with simple models that show analogous critical behaviour. The measured data allow us to fit the critical exponents finding values in agreement with the mean-field prediction. The location of the critical point and the slope of the first-order line are accurately measured.

An FPGA-Based Supercomputer for Statistical Physics: The Weird Case of Janus

Abstract We study SU(2) lattice gauge theory in small volumes and with twist m = (1, 1, 1) . We investigate the presence of the periodic instantons of Q = 1 2 and determine their free energy and their contribution to the splitting of energy flux sectors E( e = (1, 1, 1)) − E( e = (0, 0, 0)) .

Dynamical generation of a gauge symmetry in the double-exchange model

Abstract We simulate the compact U(1)-Higgs model in a four-dimensional lattice. We present a numerical study for the behaviour around the region where the transition between the confining and Higgs phases disappears. The transition line is found to be first order and to end in a second-order point. We measure the critical exponents of the endpoint obtaining the mean field ones within errors.