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Critical exponents and equation of state of the threedimensional Heisenberg universality class,” condmat/0110336
"... We improve the theoretical estimates of the critical exponents for the threedimensional Heisenberg universality class. We find γ = 1.3960(9), ν = 0.7112(5), η = 0.0375(5), α = −0.1336(15), β = 0.3689(3), and δ = 4.783(3). We consider an improved lattice φ 4 Hamiltonian with suppressed leading scalin ..."
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We improve the theoretical estimates of the critical exponents for the threedimensional Heisenberg universality class. We find γ = 1.3960(9), ν = 0.7112(5), η = 0.0375(5), α = −0.1336(15), β = 0.3689(3), and δ = 4.783(3). We consider an improved lattice φ 4 Hamiltonian with suppressed leading scaling corrections. Our results are obtained by combining Monte Carlo simulations based on finitesize scaling methods and hightemperature expansions. The critical exponents are computed from hightemperature expansions specialized to the φ 4 improved model. By the same technique we determine the coefficients of the smallmagnetization expansion of the equation of state. This expansion is extended analytically by means of approximate parametric representations, obtaining the equation of state in the whole critical region. We also determine a number of universal amplitude ratios. PACS Numbers: 75.10.Hk, 75.10.–b, 05.70.Jk, 11.15.Me Typeset using REVTEX 1 TABLE I. Recent experimental estimates of the critical exponents for Heisenberg systems.
Simulating spin models on GPU
"... Over the last couple of years it has been realized that the vast computational power of graphics processing units (GPUs) could be harvested for purposes other than the video game industry. This power, which at least nominally exceeds that of current CPUs by large factors, results from the relative s ..."
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Over the last couple of years it has been realized that the vast computational power of graphics processing units (GPUs) could be harvested for purposes other than the video game industry. This power, which at least nominally exceeds that of current CPUs by large factors, results from the relative simplicity of the GPU architectures as compared to CPUs, combined with a large number of parallel processing units on a single chip. To benefit from this setup for general computing purposes, the problems at hand need to be prepared in a way to profit from the inherent parallelism and hierarchical structure of memory accesses. In this contribution I discuss the performance potential for simulating spin models, such as the Ising model, on GPU as compared to conventional simulations on CPU.
Performance potential for simulating spin models on GPU
 Journal of Computational Physics
"... Graphics processing units (GPUs) are recently being used to an increasing degree for general computational purposes. This development is motivated by their theoretical peak performance, which significantly exceeds that of broadly available CPUs. For practical purposes, however, it is far from clear ..."
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Graphics processing units (GPUs) are recently being used to an increasing degree for general computational purposes. This development is motivated by their theoretical peak performance, which significantly exceeds that of broadly available CPUs. For practical purposes, however, it is far from clear how much of this theoretical performance can be realized in actual scientific applications. As is discussed here for the case of studying classical spin models of statistical mechanics by Monte Carlo simulations, only an explicit tailoring of the involved algorithms to the specific architecture under consideration allows to harvest the computational power of GPU systems. A number of examples, ranging from Metropolis simulations of ferromagnetic Ising models, over continuous Heisenberg and disordered spinglass systems to paralleltempering simulations are discussed. Significant speedups by factors of up to 1000 compared to serial CPU code as well as previous GPU implementations are observed.
Monte Carlo Simulation of Polymers: CoarseGrained Models
"... Permission to make digital or hard copies of portions of this work for personal or classroom use is granted provided that the copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise requires pri ..."
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Permission to make digital or hard copies of portions of this work for personal or classroom use is granted provided that the copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise requires prior specific permission by the publisher mentioned above.
Critical Dynamics in Thin Films
 J. Stat. Phys
, 2006
"... Critical dynamics in film geometry is analyzed within the fieldtheoretical approach. In particular we consider the case of purely relaxational dynamics (Model A) and Dirichlet boundary conditions, corresponding to the socalled ordinary surface universality class on both confining boundaries. The g ..."
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Critical dynamics in film geometry is analyzed within the fieldtheoretical approach. In particular we consider the case of purely relaxational dynamics (Model A) and Dirichlet boundary conditions, corresponding to the socalled ordinary surface universality class on both confining boundaries. The general scaling properties for the linear response and correlation functions and for dynamic Casimir forces are discussed. Within the Gaussian approximation we determine the analytic expressions for the associated universal scaling functions and study quantitatively in detail their qualitative features as well as their various limiting behaviors close to the bulk critical point. In addition we consider the effects of timedependent fields on the fluctuationinduced dynamic Casimir force and determine analytically the corresponding universal scaling functions and their asymptotic behaviors for two specific instances of instantaneous perturbations. The universal aspects of nonlinear relaxation from an initially ordered state are also discussed emphasizing the different crossovers that occur during this evolution. The model considered is relevant to the critical dynamics of actual uniaxial ferromagnetic films with symmetrypreserving conditions at the confining
Dynamic critical behavior of an extended reptation dynamics for selfavoiding walks
 Phys. Rev. E
, 2002
"... We consider lattice selfavoiding walks and discuss the dynamic critical behavior of two dynamics that use local and bilocal moves and generalize the usual reptation dynamics. We determine the integrated and exponential autocorrelation times for several observables, perform a dynamic finitesize sca ..."
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We consider lattice selfavoiding walks and discuss the dynamic critical behavior of two dynamics that use local and bilocal moves and generalize the usual reptation dynamics. We determine the integrated and exponential autocorrelation times for several observables, perform a dynamic finitesize scaling study of the autocorrelation functions, and compute the associated dynamic critical exponents z. For the variables that describe the size of the walks, in the absence of interactions we find z ≈ 2.2 in two dimensions and z ≈ 2.1 in three dimensions. At the θpoint in two dimensions we have z
Hightemperature series for the bonddiluted Ising model in 3, 4, and class of 3D sitediluted and bonddiluted Ising systems 45 5 dimensions
, 2006
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Quenched disordered ferromagnets
 in Proceedings of “Lattice 2005 Dublin”, PoS, p. 018, PoS(LAT2005)018
, 2005
"... We review and compare different approaches for studying the influence of quenched, random disorder in threedimensional Ising and Potts models for ferromagnets subject to impurities. From a theoretical view point, field theoretic renormalization group studies provide quite accurate results. Experime ..."
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We review and compare different approaches for studying the influence of quenched, random disorder in threedimensional Ising and Potts models for ferromagnets subject to impurities. From a theoretical view point, field theoretic renormalization group studies provide quite accurate results. Experiments carried out on crystalline mixtures of compounds lead to measurements of criticial exponents as accurate as three digits. Numerically, extensive Monte Carlo simulations are shown to be of comparable accuracy. Finally, we also discuss recently generated hightemperature series expansions for the free energy and susceptibility. Within this approach, using the stargraph expansion technique, quenched disorder averages can be calculated exactly while keeping the disorder strength p as well as the dimension d as symbolic parameters.