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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: Numerical results on the low temperature properties of the dipolar spin ice model are reported, obtained via a new loop algorithm which greatly improves the dynamics at low temperature.
Abstract: It has recently been suggested that long-range magnetic dipolar interactions are responsible for spin ice behavior in the Ising pyrochlore magnets Dy2Ti2O7 and Ho2Ti2O7. We report here numerical results on the low temperature properties of the dipolar spin ice model, obtained via a new loop algorithm which greatly improves the dynamics at low temperature. We recover the previously reported missing entropy in this model, and find a first order transition to a long-range ordered phase with zero total magnetization at very low temperature. We discuss the relevance of these results to Dy2Ti2O7 and Ho2Ti2O7.
242 citations
Journal Article•
TL;DR: Some recent theoretical efforts in calculating this nontrivial exponent in various models are reviewed and some recent experiments that measured this exponent are mentioned, mentioning the emerging new directions towards different generalizations of persistence.
Abstract: THE problem of persistence in spatially extended nonequilibrium systems has recently generated a lot of interest both theoretically and experimentally. Persistence is simply the probability that the local value of the fluctuating nonequilibrium field does not change sign up to time t. It has been studied in various systems, including several models undergoing phase separation, the simple diffusion equation with random initial conditions, several reaction diffusion systems in both pure and disordered environments, fluctuating interfaces, Lotka–Volterra models of population dynamics, and granular media. The precise definition of persistence is as follows. Let φ(x, t) be a nonequilibrium field fluctuating in space and time according to some dynamics. For example, it could represent the coarsening spin field in the Ising model after being quenched to low temperature from an initial high temperature. It could also be simply a diffusing field starting from random initial configuration or the height of a fluctuating interface. Persistence is simply the probability P0(t) that at a fixed point in space, the quantity sgn[φ(x, t) – 〈φ(x, t)〉] does not change up to time t. In all the examples mentioned above this probability decays as a power law P0(t) ~ t –θ at late times, where the persistence exponent θ is usually nontrivial. In this article, we review some recent theoretical efforts in calculating this nontrivial exponent in various models and also mention some recent experiments that measured this exponent. The plan of the paper is as follows. We first discuss the persistence in very simple single variable systems. This makes the ground for later study of persistence in more complex many-body systems. Next, we consider many-body systems such as the Ising model and discuss where the complexity is coming from. We follow it up with the calculation of this exponent for a simpler manybody system namely diffusion equation and see that even in this simple case, the exponent θ is nontrivial. Next, we show that all these examples can be viewed within the general framework of the ‘zero crossing’ problem of a Gaussian stationary process (GSP). We review the new results obtained for this general Gaussian problem in various special cases. Finally, we mention the emerging new directions towards different generalizations of persistence. We start with a very simple system namely the onedimensional Brownian walker. Let φ(t) represent the position of a 1-D Brownian walker at time t. This is a single-body system in the sense that the field φ has no x dependence but only t dependence. The position of the walker evolves as,
242 citations
TL;DR: This work proposes a new approach towards analytically solving for the dynamical content of conformal field theories (CFTs) using the bootstrap philosophy, and illustrates the power of this method in the ε expansion of the Wilson-Fisher fixed point by reproducing anomalous dimensions and obtaining OPE coefficients to higher orders in ε than currently available using other analytic techniques.
Abstract: We propose a new approach towards analytically solving for the dynamical content of conformal field theories (CFTs) using the bootstrap philosophy. This combines the original bootstrap idea of Polyakov with the modern technology of the Mellin representation of CFT amplitudes. We employ exchange Witten diagrams with built-in crossing symmetry as our basic building blocks rather than the conventional conformal blocks in a particular channel. Demanding consistency with the operator product expansion (OPE) implies an infinite set of constraints on operator dimensions and OPE coefficients. We illustrate the power of this method in the. expansion of the Wilson-Fisher fixed point by reproducing anomalous dimensions and, strikingly, obtaining OPE coefficients to higher orders in. than currently available using other analytic techniques (including Feynman diagram calculations). Our results enable us to get a somewhat better agreement between certain observables in the 3D Ising model and the precise numerical values that have been recently obtained.
241 citations
TL;DR: The stationary critical properties of the isotropic majority vote model on a square lattice were calculated by Monte Carlo simulations and finite size analysis as mentioned in this paper, and the critical exponentsν, γ, and β were found to be the same as those of the Ising model and critical noise parameter was qc=0.075±0.001.
Abstract: The stationary critical properties of the isotropic majority vote model on a square lattice are calculated by Monte Carlo simulations and finite size analysis. The critical exponentsν, γ, andβ are found to be the same as those of the Ising model and the critical noise parameter is found to beqc=0.075±0.001.
241 citations
TL;DR: In this article, the authors investigated three Ising models on the simple cubic lattice by means of Monte Carlo methods and finite-size scaling, and found that the correction-to-scaling amplitudes are strongly dependent on the introduction of further-neighbour interactions or a third spin state.
Abstract: We investigate three Ising models on the simple cubic lattice by means of Monte Carlo methods and finite-size scaling. These models are the spin-1/2 Ising model with nearest-neighbour interactions, a spin-1/2 model with nearest-neighbour and third-neighbour interactions, and a spin-1 model with nearest-neighbour interactions. The results are in accurate agreement with the hypothesis of universality. Analysis of the finite-size scaling behaviour reveals corrections beyond those caused by the leading irrelevant scaling field. We find that the correction-to-scaling amplitudes are strongly dependent on the introduction of further-neighbour interactions or a third spin state. In a spin-1 Ising model, these corrections appear to be very small. This is very helpful for the determination of the universal constants of the Ising model. The renormalization exponents of the Ising model are determined as yt=1.587 (2), yh=2.4815 (15) and yi=-0.82 (6). The universal ratio Q=(m2)2/(m4) is equal to 0.6233 (4) for periodic systems with cubic symmetry. The critical point of the nearest-neighbour spin-1/2 model is Kc=0.2216546 (10).
241 citations