Ising model

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

Real-space renormalization group calculations for spin glasses and dilute magnets

Abstract: The Edwards and Anderson model for spin glasses is investigated by a decimation rescaling transformation applied to a spin-1/2 Ising model The technique reproduces the exactly known results for a linear chain and, in particular, predicts ordering to a spin-glass type ground state at T=0 For a two-dimensional square lattice it is shown that approximations which give qualitatively correct results in other situations predict no spin-glass transition at any temperature A comparison is made with results for spin glasses on a Bethe lattice and with an infinite-range spin-glass model, which has been found to exhibit a transition It is argued that the difference between infinite-range and short-range models is that the former has entirely extended eigenvectors of the random Jij matrix whereas the latter has at least some localized eigenvectors

The Low-Temperature Expansion of the Wulff Crystal in the 3D Ising Model

Abstract: We compute the expansion of the surface tension of the 3D random cluster model for q≥ 1 in the limit where p goes to 1. We also compute the asymptotic shape of a plane partition of n as n goes to ∞. This same shape determines the Wulff crystal to order o(ɛ) in the 3D Ising model (and more generally in the 3D random cluster model for q≥ 1) at temperature ɛ.

Small-world phenomena in physics: the Ising model

Abstract: The Ising system with a small fraction of random long-range interactions is the simplest example of small-world phenomena in physics. Considering the latter both in an annealed and in a quenched state we conclude that: (a) the existence of random long-range interactions leads to a phase transition in the one-dimensional case and (b) there is a minimal average number p of these interactions per site (p<1 in the annealed state, and p1 in the quenched state) needed for the appearance of the phase transition. Note that the average number of these bonds, pN/2, is much smaller than the total number of bonds, N2/2.

A Conformal Dispersion Relation: Correlations from Absorption

Abstract: We introduce the analog of Kramers-Kronig dispersion relations for correlators of four scalar operators in an arbitrary conformal field theory. The correlator is expressed as an integral over its “absorptive part”, defined as a double discontinuity, times a theory-independent kernel which we compute explicitly. The kernel is found by resumming the data obtained by the Lorentzian inversion formula. For scalars of equal scaling dimensions, it is a remarkably simple function (elliptic integral function) of two pairs of cross-ratios. We perform various checks of the dispersion relation (generalized free fields, holographic theories at tree-level, 3D Ising model), and get perfect matching. Finally, we derive an integral relation that relates the “inverted” conformal block with the ordinary conformal block.