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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 existence and the conformal invariance of scaling limits of the magnetization and multi-point spin correlations in the critical Ising model on arbitrary simply connected planar domains were proved.
Abstract: We rigorously prove the existence and the conformal invariance of scaling limits of the magnetization and multi-point spin correlations in the critical Ising model on arbitrary simply connected planar domains. This solves a number of conjectures coming from the physical and the mathematical literature. The proof relies on convergence results for discrete holomorphic spinor observables and probabilistic techniques.
150 citations
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TL;DR: In this paper, the authors derived the phenomenological dynamics of interfaces from stochastic "microscopic" models and derived Green-Kubo-like expressions for the mobility.
Abstract: We derive the phenomenological dynamics of interfaces from stochastic “microscopic” models. The main emphasis is on models with a nonconserved order parameter. A slowly varying interface has then a local normal velocity proportional to the local mean curvature. We study bulk models and effective interface models and obtain Green-Kubo-like expressions for the mobility. Also discussed are interface motion in the case of a conserved order parameter, pure surface diffusion, and interface fluctuations. For the two-dimensional Ising model at zero temperature, motion by mean curvature is established rigorously.
149 citations
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TL;DR: In this article, a correspondence between Eigen's model of macromolecular evolution and the equilibrium statistical mechanics of an inhomogeneous Ising system is developed, where the free energy landscape of random Ising systems with the Hopfield Hamiltonian as a special example is applied to the replication rate coefficient landscape.
Abstract: The correspondence between Eigen's model of macromolecular evolution and the equilibrium statistical mechanics of an inhomogeneous Ising system is developed. The free energy landscape of random Ising systems with the Hopfield Hamiltonian as a special example is applied to the replication rate coefficient landscape. The coupling constants are scaled with 1/l, since the maxima of any landscape must not increase with the length of the macromolecules. The calculated error threshold relation then agrees with Eigen's expression, which was derived in a different way. It gives an explicit expression for the superiority parameter in terms of the parameters of the landscape. The dynamics of selection and evolution is discussed.
149 citations
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TL;DR: In this paper, the authors studied the chiral Ising, chiral XY, and chiral Heisenberg models at four-loop order with the perturbative renormalization group in $4\ensuremath{-}\enuremath{\epsilon}$ dimensions and computed critical exponents for the Gross-Neveu-Yukawa fixed points.
Abstract: We study the chiral Ising, the chiral XY, and the chiral Heisenberg models at four-loop order with the perturbative renormalization group in $4\ensuremath{-}\ensuremath{\epsilon}$ dimensions and compute critical exponents for the Gross-Neveu-Yukawa fixed points to order $\mathcal{O}({\ensuremath{\epsilon}}^{4})$. Further, we provide Pad\'e estimates for the correlation length exponent, the boson and fermion anomalous dimension, as well as the leading correction to scaling exponent in $2+1$ dimensions. We also confirm the emergence of supersymmetric field theories at four loops for the chiral Ising and the chiral XY models with $N=1/4$ and $N=1/2$ fermions, respectively. Furthermore, applications of our results relevant to various quantum transitions in the context of Dirac and Weyl semimetals are discussed, including interaction-induced transitions in graphene and surface states of topological insulators.
149 citations
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TL;DR: In this paper, the Lee-Yang theorem for the zeros of the partition function of a ferromagnetic Ising model with real pair spin interactions is extended to general Ising models with complex many-spin interactions.
Abstract: The Lee‐Yang theorem for the zeros of the partition function of a ferromagnetic Ising model with real pair spin interactions is extended to general Ising models with complex many‐spin interactions (satisfying appropriate ``ferromagnetic'' and spin inversion symmetry conditions). When many‐spin interactions are present, all zeros lie on the imaginary Hz‐axis for sufficiently low (but fixed) T, but, in general, some leave the imaginary axis as T → ∞. The extended Ising theorem is used to prove the same result for a Heisenberg system of arbitrary spin with the real anisotropic pair interaction Hamiltonian Hij=−(JijzSizSjz+JijxSixSjx+JijySiySjy) in an arbitrary transverse field (Hx, Hy) under the ``ferromagnetic'' condition Jijz≥|Jijx| and Jijz≥|Jijy|. The analyticity of the limiting free energy of such a Heisenberg ferromagnet and the absence of a phase transition are thereby established for all (real) nonzero magnetic fields Hz. The Ising theorem is also applied to hydrogen‐bonded ferroelectric models to prove, in particular, that the zeros for the KDP model lie on the imaginary electric field axis for all T below the transition temperature Tc.
149 citations