Open Access
Worm Algorithms for Classical Statistical Models
Nikolay Prokof'ev,Boris Svistunov,Boris Svistunov +2 more
- 01 Mar 2002
15
TL;DR: In this article, high-temperature expansions provide a basis for efficient Monte Carlo simulations, and the authors show that local, Metropolis-type schemes using this approach appear to have dynamical critical exponents close to zero (i.e., their efficiency is comparable to the best cluster methods).
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Abstract: We show that high-temperature expansions provide a basis for the novel approach to efficient Monte Carlo simulations. "Worm" algorithms utilize the idea of updating closed-path configurations (produced by high-temperature expansions) through the motion of end points of a disconnected path. An amazing result is that local, Metropolis-type schemes using this approach appear to have dynamical critical exponents close to zero (i.e., their efficiency is comparable to the best cluster methods) as proved by finite-size scaling of the autocorrelation time for various universality classes.
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Citations
Optimized Broad-Histogram Ensembles for the Simulation of Quantum Systems
TL;DR: How a recently developed feedback algorithm can be generalized to find optimized sampling distributions for the simulation of quantum systems in the context of the stochastic series expansion (SSE) when defining an extended ensemble in the expansion order is described.
13
Transforming Generalized Ising Model into Boltzmann Machine
Nobuyuki Yoshioka,Yutaka Akagi,Hosho Katsura +2 more
- 16 Apr 2019
TL;DR: It is demonstrated that the application of the method in conjunction with the Swendsen-Wang algorithm drastically reduces the critical slowing down in a model with two- and three-spin interactions on the Kagomé lattice.
7
Structure and Diffraction Properties of Disordered Systems
David Heinrich Wojtas
- 01 Jan 2011
TL;DR: In this article, the authors investigated the correlation behavior of two geometrically frustrated systems, the triangular Ising antiferromagnet (TIA) and the fully frustrated square Ising model (FFS), and its use to interpret X-ray fiber diffraction patterns.
6
Monte Carlo Simulation Study of 1D Josephson Junction Arrays
Oliver Nikolic
- 01 Jan 2016
TL;DR: In this article, the effect of inducing charge by connecting an external voltage source to one island in the chain via the ground capacitance is investigated, and Monte Carlo simulations of this model can be constructed based on the worm algorithm with efficiency comparable to the best cluster algorithms.
6
O(3) model with Nienhuis action
Ferenc Niedermayer,Ulli Wolff +1 more
- 27 Dec 2016
TL;DR: In this article, the authors studied the O(3) sigma model with a Boltzmann weight linearized in β$ on each link and showed that the mass gap coupling still has the right universal continuum limit.
References
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Shang-keng Ma
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TL;DR: The examination of phase transitions and critical phenomena has dominated statistical physics for the latter half of this century--there is a great theoretical challenge in solving special statistical mechanical models and beautiful experimental results have elucidated the singularities in phase transitions.
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Statistical Field Theory
Giorgio Parisi,Ramamurti Shankar +1 more
TL;DR: Classical equilibrium statistical mechanics magnetic systems the Ising model the lowtemperature and high-temperature expansions the Landau-Ginsberg model near the transition the renormalization group perturbative evaluation of the critical exponents near four dimensions on spontaneous symmetry breaking other models as discussed by the authors.
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The loop algorithm
TL;DR: The loop algorithm as mentioned in this paper is a quantum Monte Carlo procedure that employs non-local changes of worldline configurations, determined by local stochastic decisions, and is related to Swendsen-Wang algorithms.
Principal problems in Bose-Einstein condensation of dilute gases
TL;DR: A survey of the state of the art in studying Bose-Einstein condensation of dilute atomic gases is given in this article, with the bulk of attention focused on the principal theoretical problems, though the related experiments are also mentioned.
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