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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: It is concluded that, contrary to theoretical expectations, quantum transitions can be qualitatively different from thermally driven transitions in real spin glasses.
Abstract: LiHo_(0.167)Y_(0.833)F_4 is a dilute dipolar-coupled Ising magnet with a spin glass transition which can be crossed with temperature T (T_g=0.13 K) or with an effective transverse field Γ(Γ_g=1 K at T=0). The nonlinear susceptibility contains a diverging component which dominates at T=98 mK, but disappears by 25 mK. At the same time, the onset of spin glass behavior in the dissipative linear susceptibility becomes sharper. We conclude that, contrary to theoretical expectations, quantum transitions can be qualitatively different from thermally driven transitions in real spin glasses.
113 citations
TL;DR: In this article, the Ising model of ferromagnetism is examined in the limit of high density in the anticipation that one recovers the Weiss molecular field in the case of infinite density.
Abstract: The partition function of the Ising model of ferromagnetism is examined in the limit of high density in the anticipation that in the limit of infinite density one recovers the Weiss molecular field. The formal parameter of expansion is $\frac{1}{z}$ where $z$ is the number of spins in the range of the exchange potential (not restricted to nearest neighbor interactions). In the absence of long-range order, only ring diagrams in the cluster expansion contribute. These give a divergence in the specific heat at $k{T}_{c}=\ensuremath{\Sigma}{j\ensuremath{
e}i}^{}{v}_{\mathrm{ij}}$ where ${v}_{\mathrm{ij}}$ is the exchange potential. This is the molecular field value for the Curie point ${T}_{c}$. In the presence of a magnetic field the partition function is evaluated for fixed magnetic moment $M$ in the same approximation, $M$ being determined by minimization. This results in a susceptibility differing from the molecular field theory and hence an inconsistency in the theory.
113 citations
TL;DR: In this paper, the authors describe an approach to logarithmic conformal field theories as limits of sequences of ordinary conformal fields theories with varying central charge c. The theories are all invariant under some internal symmetry group, and log-scale behaviour occurs when the decomposition of the physical observables into irreducible operators becomes singular.
Abstract: We describe an approach to logarithmic conformal field theories as limits of sequences of ordinary conformal field theories with varying central charge c. Logarithmic behaviour arises from degeneracies in the spectrum of scaling dimensions at certain values of c. The theories we consider are all invariant under some internal symmetry group, and logarithmic behaviour occurs when the decomposition of the physical observables into irreducible operators becomes singular. Examples considered are quenched random magnets using the replica formalism, self-avoiding walks as the n->0 of the O(n) model, and percolation as the limit Q->1 of the Potts model. In these cases we identify logarithmic operators and pay particular attention to how the c->0 paradox is resolved and how the b-parameter is evaluated. We also show how this approach gives information on logarithmic behaviour in the extended Ising model, uniform spanning trees and the O(-2) model. Most of our results apply to general dimensionality. We also consider massive logarithmic theories and, in two dimensions, derive sum rules for the effective central charge and the b-parameter.
113 citations
TL;DR: In this article, an exact numerical method is used to reveal the properties of a model exhibiting a quantum phase transition between an isotropic and a nematic metal, and it is shown that some of the remarkable behaviors of strongly correlated metals may be controlled by quantum phase transitions.
Abstract: Some of the remarkable behaviors of strongly correlated metals may be controlled by quantum phase transitions. An exact numerical method is used to reveal the properties of a model exhibiting a quantum phase transition between an isotropic and a nematic metal.
113 citations
TL;DR: In this paper, Wu et al. showed that (2n+1) is singular on the unit circle at sk = exp(ik) where 2cos(k) = cos(2 k/(2 n+1))+cos(2/(2n + 1))+ cos( 2 n+ 1)), -n k, n. The singularities, k = 0 excepted, are logarithmic branch points of order 2n(n+ 1)-1ln() with = 1-s/sk.
Abstract: Some simplifications of the integrals (2n+1), derived by Wu et al (1976 13 316), that contribute to the zero field susceptibility of the 2D square lattice Ising model are reported. In particular, several alternate expressions for the integrands in (2n+1) are determined which greatly facilitate both the generation of high-temperature series and analytical analysis. One can show that as series, (2n+1) = 22n(s/2)4n(n+1)(1+O(s)) where s is the high-temperature variable sin(2K) with K the conventional normalized inverse temperature. Analysis of the integrals near symmetry points of the integrands shows that (2n+1)(s) is singular on the unit circle at sk = exp(ik) where 2cos(k) = cos(2 k/(2n+1))+cos(2/(2n+1)), -n k, n. The singularities, k = 0 excepted, are logarithmic branch points of order 2n(n+1)-1ln() with = 1-s/sk. There is numerical evidence from series that these van Hove points, in addition to the known points at s = ?1 and ?i, exhaust the singularities on the unit circle. Barring cancellation from extra (unobserved) singularities one can conclude that |s| = 1 is a natural boundary for the susceptibility.
113 citations