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Ising model

About: Ising model is a research topic. Over the lifetime, 25508 publications have been published within this topic receiving 555000 citations.


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TL;DR: In this article, the authors used finite-size scaling techniques to obtain accurate results for critical quantities of the Ising model and the site percolation, in three dimensions, and paid special attention to parametrizing the corrections-to-scaling, which was necessary to bring the systematic errors below the statistical ones.
Abstract: Using finite-size scaling techniques we obtain accurate results for critical quantities of the Ising model and the site percolation, in three dimensions. We pay special attention to parametrizing the corrections-to-scaling, which is necessary to bring the systematic errors below the statistical ones.

163 citations

Journal ArticleDOI
TL;DR: In this paper, the authors considered the metastable behavior of a ferromagnetic spin system with a Glauber dynamics in a finite two-dimensional torus under a positive magnetic field in the limit as the temperature goes to zero.
Abstract: We consider the metastable behavior in the so-called pathwise approach of a ferromagnetic spin system with a Glauber dynamics in a finite two dimensional torus under a positive magnetic field in the limit as the temperature goes to zero. First we consider the evolution starting from a single rectangular droplet of spins +1 in a sea of spins −1. We show that small droplets are likely to disappear while large droplets are likely to grow; the threshold between the two cases being sharply defined and depending only on the external field. This result is used to prove that starting from the configuration with all spins down (−1) the pattern of evolution leading to the more stable configuration with all spins up (+1) approaches, as the temperature vanishes, a metastable behavior: the system stays close to −1 for an unpredictable time until a critical square droplet of a precise size is eventually formed and nucleates the decay to +1 in a relatively short time. The asymptotic magnitude of the total decay time is shown to be related to the height of an energy barrier, as expected from heuristic and mean field studies of metastability.

163 citations

Journal ArticleDOI
TL;DR: In this article, the percolation behavior of spherical particles with attractive interactions is studied with use of Monte Carlo simulations, and the simulation results are discussed in the light of recent experiments which measure the temperature and concentration dependence of the conductivity in interacting microemulsions.
Abstract: The percolation behavior of spherical particles with attractive interactions is studied with use of Monte Carlo simulations. These systems differ from lattice Ising systems, which have been previously analyzed, in the necessity to define a shell parameter \ensuremath{\delta} to specify a connected cluster. For small values of \ensuremath{\delta}, correlations due to the attractive interactions drastically lower the percolation threshold in the vicinity of the gas-liquid critical point. For larger values of \ensuremath{\delta}, these shifts are smaller, but the effects of long-range correlations show up as enhanced finite-size effects. The simulation results are discussed in the light of recent experiments which measure the temperature and concentration dependence of the conductivity in interacting microemulsions.

163 citations

Journal ArticleDOI
TL;DR: A novel method for the calculation of the energy density of states D(E) for systems described by classical statistical mechanics using an extension of a recently proposed strategy that allows the free-energy profile of a canonical system to be recovered within a preassigned accuracy.
Abstract: We present a novel method for the calculation of the energy density of states $D(E)$ for systems described by classical statistical mechanics. The method builds on an extension of a recently proposed strategy that allows the free-energy profile of a canonical system to be recovered within a preassigned accuracy [A. Laio and M. Parrinello, Proc. Natl. Acad. Sci. U.S.A. 99, 12562 (2002)]. The method allows a good control over the error on the recovered system entropy. This fact is exploited to obtain $D(E)$ more efficiently by combining measurements at different temperatures. The accuracy and efficiency of the method are tested for the two-dimensional Ising model (up to size $50\ifmmode\times\else\texttimes\fi{}50$) by comparison with both exact results and previous studies. This method is a general one and should be applicable to more realistic model systems.

163 citations

Journal ArticleDOI
TL;DR: In this paper, a small-correlation expansion was proposed to solve the inverse Ising problem and find a set of couplings and fields corresponding to a given set of correlations and magnetizations.
Abstract: We present a systematic small-correlation expansion to solve the inverse Ising problem and find a set of couplings and fields corresponding to a given set of correlations and magnetizations. Couplings are calculated up to the third order in the correlations for generic magnetizations and to the seventh order in the case of zero magnetizations; in addition, we show how to sum some useful classes of diagrams exactly. The resulting expansion outperforms existing algorithms on the Sherrington–Kirkpatrick spin-glass model.

162 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023682
20221,314
2021854
2020947
2019870
2018844