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Chain length probability distribution - equivalence of ASYNNNI and 1d Ising model

100%
Milić M.
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vol. 6
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issue 2
311-316
EN
An expression for the chain length probability distribution p(l) of a one dimensional Ising chain was derived using the cluster variation method formalism, the p(l) being expressed through the pair cluster probabilities. It was shown numerically that the same expression also applies in the case of one dimensional chains formed along one of the next-nearest neighbor interactions included in the two dimensional ASYNNNI (Asymmetric Next-Nearest Neighbor Ising) model, widely used to describe the statistics of oxygen ordering in the basal CuOx planes of the YBa2Cu3O6+x type high-Tc superconducting materials. Equivalency between ASYNNNI and 1d Ising model is discussed.
2
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The Test of a New Critical Exponent Ϙ by Using Ising Model on the Creutz Cellular Automaton

88%
Merdan Z., Gokbel-Keklikoglu D.
Acta Physica Polonica A
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2018
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vol. 133
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issue 5
1200-1204
EN
Above the upper critical dimension d_{c} the Ising model is simulated on the Creutz cellular automaton. The values of a new critical exponent Ϙ are obtained by using the simulations for the order parameter and the magnetic susceptibility. At d=4,5,6,7,8, the values of the new critical exponent Ϙ are 0.9904(16), 1.2721(2), 1.4806(24), 1.7626(17), 1.9997(50) for the order parameter, respectively, while those 1.0415(13), 1.2987(27), 1.5133(1), 1.7741(1), 2.0133(28) are for the magnetic susceptibility in the same order. The computed values of the new critical exponent Ϙ are in agreement with theoretical values.
3
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Reconstruction of the finite size canonical ensemble from incomplete micro-canonical data

88%
Lundow P., Markström K.
Open Physics
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2009
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vol. 7
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issue 3
490-502
EN
In this paper we discuss how partial knowledge of the density of states for a model can be used to give good approximations of the energy distributions in a given temperature range. From these distributions one can then obtain the statistical moments corresponding to e.g. the internal energy and the specific heat. These questions have gained interest apropos of several recent methods for estimating the density of states of spin models. As a worked example we finally apply these methods to the 3-state Potts model for cubic lattices of linear order up to 128. We give estimates of e.g. latent heat and critical temperature, as well as the micro-canonical properties of interest.
4
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Can Ising model and/or QKPZ equation properly describe reactive-wetting interface dynamics?

75%
Efraim Y., Taitelbaum H.
Open Physics
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2009
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vol. 7
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issue 3
503-508
EN
The reactive-wetting process, e.g. spreading of a liquid droplet on a reactive substrate is known as a complex, non-linear process with high sensitivity to minor fluctuations. The dynamics and geometry of the interface (triple line) between the materials is supposed to shed light on the main mechanisms of the process. We recently studied a room temperature reactive-wetting system of a small (∼ 150 μm) Hg droplet that spreads on a thin (∼ 4000 Å) Ag substrate. We calculated the kinetic roughening exponents (growth and roughness), as well as the persistence exponent of points on the advancing interface. In this paper we address the question whether there exists a well-defined model to describe the interface dynamics of this system, by performing two sets of numerical simulations. The first one is a simulation of an interface propagating according to the QKPZ equation, and the second one is a landscape of an Ising chain with ferromagnetic interactions in zero temperature. We show that none of these models gives a full description of the dynamics of the experimental reactivewetting system, but each one of them has certain common growth properties with it. We conjecture that this results from a microscopic behavior different from the macroscopic one. The microscopic mechanism, reflected by the persistence exponent, resembles the Ising behavior, while in the macroscopic scale, exemplified by the growth exponent, the dynamics looks more like the QKPZ dynamics.
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