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Search Results: 1 - 10 of 191235 matches for " Helmut G. Katzgraber "
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Scientific Software Engineering in a Nutshell
Helmut G. Katzgraber
Physics , 2009,
Abstract: Writing complex computer programs to study scientific problems requires careful planning and an in-depth knowledge of programming languages and tools. In this chapter the importance of using the right tool for the right problem is emphasized. Common tools to organize computer programs, as well as to debug and improve them are discussed, followed by simple data reduction strategies and visualization tools. Furthermore, some useful scientific libraries such as boost, GSL, LEDA and numerical recipes are outlined.
Introduction to Monte Carlo Methods
Helmut G. Katzgraber
Physics , 2009,
Abstract: Monte Carlo methods play an important role in scientific computation, especially when problems have a vast phase space. In this lecture an introduction to the Monte Carlo method is given. Concepts such as Markov chains, detailed balance, critical slowing down, and ergodicity, as well as the Metropolis algorithm are explained. The Monte Carlo method is illustrated by numerically studying the critical behavior of the two-dimensional Ising ferromagnet using finite-size scaling methods. In addition, advanced Monte Carlo methods are described (e.g., the Wolff cluster algorithm and parallel tempering Monte Carlo) and illustrated with nontrivial models from the physics of glassy systems. Finally, we outline an approach to study rare events using a Monte Carlo sampling with a guiding function.
Numerical studies of the 2 and 3D gauge glass at low temperature
Helmut G. Katzgraber
Physics , 2003, DOI: 10.1063/1.1538177
Abstract: We report results from Monte Carlo simulations of the two- and three-dimensional gauge glass at low temperature using parallel tempering Monte Carlo. In two dimensions, we find strong evidence for a zero-temperature transition. By means of finite-size scaling, we determine the stiffness exponent theta = -0.39 +/- 0.03. In three dimensions, where a finite-temperature transition is well established, we find theta = 0.27 +/- 0.01, compatible with recent results from domain-wall renormalization group studies.
Random Numbers in Scientific Computing: An Introduction
Helmut G. Katzgraber
Physics , 2010,
Abstract: Random numbers play a crucial role in science and industry. Many numerical methods require the use of random numbers, in particular the Monte Carlo method. Therefore it is of paramount importance to have efficient random number generators. The differences, advantages and disadvantages of true and pseudo random number generators are discussed with an emphasis on the intrinsic details of modern and fast pseudo random number generators. Furthermore, standard tests to verify the quality of the random numbers produced by a given generator are outlined. Finally, standard scientific libraries with built-in generators are presented, as well as different approaches to generate nonuniform random numbers. Potential problems that one might encounter when using large parallel machines are discussed.
Spin glasses and algorithm benchmarks: A one-dimensional view
Helmut G. Katzgraber
Physics , 2007, DOI: 10.1088/1742-6596/95/1/012004
Abstract: Spin glasses are paradigmatic models that deliver concepts relevant for a variety of systems. However, rigorous analytical results are difficult to obtain for spin-glass models, in particular for realistic short-range models. Therefore large-scale numerical simulations are the tool of choice. Concepts and algorithms derived from the study of spin glasses have been applied to diverse fields in computer science and physics. In this work a one-dimensional long-range spin-glass model with power-law interactions is discussed. The model has the advantage over conventional systems in that by tuning the power-law exponent of the interactions the effective space dimension can be changed thus effectively allowing the study of large high-dimensional spin-glass systems to address questions as diverse as the existence of an Almeida-Thouless line, ultrametricity and chaos in short range spin glasses. Furthermore, because the range of interactions can be changed, the model is a formidable test-bed for optimization algorithms.
Monte Carlo Simulations of Vector Spin Glasses at Low Temperatures
Helmut G. Katzgraber
Physics , 2002, DOI: 10.1016/S0010-4655(02)00322-3
Abstract: In this paper I report results for simulations of the three-dimensional gauge glass and the four-dimensional XY spin glass using the parallel tempering Monte Carlo method at low temperatures for moderate sizes. The results are qualitatively consistent with earlier work on the three- and four-dimensional Edwards-Anderson Ising spin glass. I find evidence that large-scale excitations may cost only a finite amount of energy in the thermodynamic limit. The surface of these excitations is fractal, but I cannot rule out for the XY spin glass a scenario compatible with replica symmetry breaking where the surface of low-energy large-scale excitations is space filling.
On the existence of a finite-temperature transition in the two-dimensional gauge glass
Helmut G. Katzgraber
Physics , 2003, DOI: 10.1103/PhysRevB.67.180402
Abstract: Results from Monte Carlo simulations of the two-dimensional gauge glass supporting a zero-temperature transition are presented. A finite-size scaling analysis of the correlation length shows that the system does not exhibit spin-glass order at finite temperatures. These results are compared to earlier claims of a finite-temperature transition.
Universality and universal finite-size scaling functions in four-dimensional Ising spin glasses
Thomas Jorg,Helmut G. Katzgraber
Physics , 2008, DOI: 10.1103/PhysRevB.77.214426
Abstract: We study the four-dimensional Ising spin glass with Gaussian and bond-diluted bimodal distributed interactions via large-scale Monte Carlo simulations and show via an extensive finite-size scaling analysis that four-dimensional Ising spin glasses obey universality.
Evidence for universal scaling in the spin-glass phase
Thomas Jorg,Helmut G. Katzgraber
Physics , 2008, DOI: 10.1103/PhysRevLett.101.197205
Abstract: We perform Monte Carlo simulations of Ising spin-glass models in three and four dimensions, as well as of Migdal-Kadanoff spin glasses on a hierarchical lattice. Our results show strong evidence for universal scaling in the spin-glass phase in all three models. Not only does this allow for a clean way to compare results obtained from different coupling distributions, it also suggests that a so far elusive renormalization group approach within the spin-glass phase may actually be feasible.
Temperature and Disorder Chaos in Three-Dimensional Ising Spin Glasses
Helmut G. Katzgraber,Florent Krzakala
Physics , 2006, DOI: 10.1103/PhysRevLett.98.017201
Abstract: We study the effects of small temperature as well as disorder perturbations on the equilibrium state of three-dimensional Ising spin glasses via an alternate scaling ansatz. By using Monte Carlo simulations, we show that temperature and disorder perturbations yield chaotic changes in the equilibrium state and that temperature chaos is considerably harder to observe than disorder chaos.
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