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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 ground state ensemble of the pyrochlore-lattice antiferromagnet can be mapped to a coarse-grained "polarization" field satisfying a zero-divergence condition.
Abstract: The ground state ensemble of the highly frustrated pyrochlore-lattice antiferromagnet can be mapped to a coarse-grained ``polarization'' field satisfying a zero-divergence condition. From this it follows that the correlations of this field, as well as the actual spin correlations, decay with separation like a dipole-dipole interaction $(1∕\ensuremath{\mid}R{\ensuremath{\mid}}^{3})$. Furthermore, a lattice version of the derivation gives an approximate formula for spin correlations, with several features that agree well with simulations and neutron-diffraction measurements of diffuse scattering, in particular the pinch-point (pseudo-dipolar) singularities at reciprocal lattice vectors. This system is compared to others in which constraints also imply diffraction singularities, and other possible applications of the coarse-grained polarization are discussed.
175 citations
TL;DR: In this paper, low-temperature expansions for the free energy of the Ising model of a ferromagnet and an antiferromagnetic magnet were derived for the more usual two-and three-dimensional lattices.
Abstract: Low‐temperature expansions for the free energy of the Ising model of a ferromagnet and an antiferromagnet are derived for the more usual two‐ and three‐dimensional lattices. The underlying enumerative problem is studied and a new method described that makes it possible to obtain more terms than available previously without undue labor.
175 citations
TL;DR: In this paper, the authors study universality in three-dimensional Ising spin glasses by large-scale Monte Carlo simulations of the Edwards-Anderson spin glass for several choices of bond distributions, with particular emphasis on Gaussian and bimodal interactions.
Abstract: We study universality in three-dimensional Ising spin glasses by large-scale Monte Carlo simulations of the Edwards-Anderson Ising spin glass for several choices of bond distributions, with particular emphasis on Gaussian and bimodal interactions. A finite-size scaling analysis suggests that three-dimensional Ising spin glasses obey universality.
175 citations
TL;DR: In this paper, the phase diagram of the site-diluted Ising model in a wide dilution range was studied through Monte Carlo simulations and finite-size scaling techniques.
Abstract: We study the phase diagram of the site-diluted Ising model in a wide dilution range, through Monte Carlo simulations and finite-size scaling techniques. Our results for the critical exponents and universal cumulants turn out to be dilution independent, but only after a proper infinite volume extrapolation, taking into account the leading corrections-to-scaling terms.
174 citations
TL;DR: In this paper, it was shown that Baxter's recent results on a lattice-statistical model lead to the solution of an Ising model with two-and four-spin interactions.
Abstract: It is shown that Baxter's recent results on a lattice-statistical model lead to the solution of an Ising model with two- and four-spin interactions. Critical properties of this Ising model in various regions of the parameter space are given. It is argued that four-spin or crossing interactions in a two-dimensional Ising model would in general lead to a critical exponent ${\ensuremath{\alpha}}^{\ensuremath{'}}\ensuremath{
e}0$.
174 citations