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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 paper, the dependence of Markov fields on boundary conditions was studied by taking a more suitable coupling, which leads to a new uniqueness condition for Gibbs measures, in terms of disagreement percolation involving two independent realizations.
Abstract: Recently, one of the authors (van den Berg) has obtained a uniqueness condition for Gibbs measures, in terms of disagreement percolation involving two independent realizations. In the present paper we study the dependence of Markov fields on boundary conditions by taking a more suitable coupling. This coupling leads to a new uniqueness condition, which improves the one mentioned above. We also compare it with the Dobrushin uniqueness condition. In the case of the Ising model, our coupling shares certain properties with the Fortuin-Kasteleyn representation: It gives an explicit expression of the boundary effect on a certain vertex in terms of percolation-like probabilities.
124 citations
TL;DR: The relaxation time of the autocorrelation function is calculated and it is shown that the system remains paramagnetic even at zero temperature (T=0), and the fully asymmetric system is ergodic, with decaying autcorrelations, in agreement with the theoretical predictions.
Abstract: The stochastic dynamics of randomly asymmetric fully connected Ising systems is studied. We solve analytically the particularly simple case of fully asymmetric systems. We calculate the relaxation time of the autocorrelation function and show that the system remains paramagnetic even at zero temperature (T=0). The ferromagnetic phase is only slightly affected by the asymmetry, and the paramagnetic-to-ferromagnetic phase transition is characterized by a critical slowing down similar to second-order transition in symmetric (fully connected) systems. Monte Carlo simulations of a fully connected Ising system with random asymmetric interactions, both at finite and zero temperature, are presented. For finite T the autocorrelation function decays completely to zero for all strengths of the asymmetry. The T=0 behavior is more complex. In the fully asymmetric case the system is ergodic, with decaying autocorrelations, in agreement with the theoretical predictions. In the partially asymmetric case all flows terminate at fixed points (i.e., states which are stable to single spin flips). However, the typical time that it takes to converge to a fixed point grows exponentially with the size of the system. This convergence time varies from sample to sample and has a log-normal distribution in large systems. On time scales which are smaller than the convergence time, the system behaves ``ergodically,'' and the autocorrelation function decays to zero, much like the finite-temperature case.
124 citations
TL;DR: In this article, the effects of the shell coupling and the interface coupling on both the compensation temperature and the magnetization profiles are investigated, as well as their effects on the hysteresis loops.
124 citations
TL;DR: In this article, a new Monte Carlo algorithm for 2-dimensional spin glasses is presented, which allows equilibrating systems of size 1002 down to temperature T = 0.1.
Abstract: A new Monte Carlo algorithm for 2-dimensional spin glasses is presented. The use of clusters makes possible global updates and leads to a gain in speed of several orders of magnitude. As an example, we study the 2-dimensional ±J Edwards-Anderson model. The new algorithm allows us to equilibrate systems of size 1002 down to temperature T = 0.1. Our main result is that the correlation length diverges as an exponential ( ξ∼e2βJ) and not as a power law as T↦Tc = 0.
123 citations
TL;DR: In this article, the authors consider the question of conformal invariance of the long-range Ising model at the critical point and give a proof of conformality to all orders in the epsilon expansion, based on the description of the model as a defect theory in an auxiliary higher dimensional space.
123 citations