Topic
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 article, a detailed discussion of pair correlations ω2(r) = 〈σ 0σr〉 between spins at lattice sites 0 and r on the axes of anisotropic triangular lattices is given.
Abstract: A detailed discussion of pair correlations ω2(r) = 〈σ0σr〉 between spins at lattice sites 0 and r on the axes of anisotropic triangular lattices is given. The asymptotic behavior of ω2(r) for large spin separation is obtained for ferromagnetic and antiferromagnetic lattices. The axial pair correlation for the ferromagnetic triangular lattice has the same qualitative behavior as that for the ferromagnetic rectangular lattice: There is long‐range order below the Curie point TC and short‐range order above. It is shown that correlations on the anisotropic antiferromagnetic triangular lattice must be given separate treatment in three different temperature ranges. Below the Neel point TN (antiferromagnetic critical point), the completely anisotropic lattice exhibits antiferromagnetic long‐range order along the two lattice axes with the strongest interactions. Spins along the third axis with the weakest interaction are ordered ferromagnetically. Between TN and a uniquely located temperature TD, there is antiferro...
139 citations
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TL;DR: Mean field theory for one-dimensional inhomogeneous magnetic systems is formulated as an area-preserving map and its associated boundary conditions are derived for nearest-neighbor Ising interactions as discussed by the authors.
Abstract: Mean-field theory for one-dimensionally inhomogeneous magnetic systems is formulated as an area-preserving map. The map and its associated boundary conditions are derived for nearest-neighbor Ising interactions. The corresponding continuum theory is also constructed. These mappings are two dimensional. Their phase portraits are exhibited and applied to the study of a representative set of surface and interface phenomena, including interfacial structure, surface phase transitions, wetting, prewetting, and layering. The methods developed lend themselves to easy and physical visualization of the types of solutions which the mean-field theory can have, even in rather complex situations. They also make explicit the fundamental differences between continuum mean-field theory (which is integrable) and discrete mean-field theory (which is not).
138 citations
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TL;DR: Examination of the resulting structural parameters suggests that the origin of the contraction with increasing temperature can be traced straightforwardly to the rigid-body transverse librations of bridging O atoms.
Abstract: High-resolution powder diffraction data have been recorded on cubic ZrW2O8 [a = 9.18000 (3) A at 2 K] at 260 temperatures from 2 to 520 K in 2 K steps. These data have confirmed that α-ZrW2O8 has a negative coefficient of thermal expansion, α = −9.07 × 10−6 K−1 (2–350 K). A `parametric' approach to Rietveld refinement is adopted and it is demonstrated that a full anisotropic refinement can be performed at each temperature, despite using a data collection time of only 5 min. Examination of the resulting structural parameters suggests that the origin of the contraction with increasing temperature can be traced straightforwardly to the rigid-body transverse librations of bridging O atoms. α-ZrW2O8 undergoes a phase transition from P213 to Pa3¯ at 448 K that is associated with the onset of considerable oxygen mobility. The phase transition can be described in terms of a simple cubic three-dimensional Ising model. Unusual kinetics are associated with this phase transition. Hysteresis in the cell parameter through the phase transition is the opposite of that normally observed.
138 citations
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TL;DR: In this paper, the Bethe-based method is used to calculate the density matrix of a duster exactly without the perturbation method, and it is shown that the magnetization of the sublattice is completely saturated at OOK in just the same way as in the Ising model.
Abstract: based on Heisenberg model is developed by a method which is much more directly the analogue of the original B~the method than Weiss-Li's. By the present method, the calculations can be carried out over all temperatures. Especially, the situation at lower temperatures which is obscure in Weiss·U's papers is made dear. Thus we can see that an anti·Curie point which Anderson has proposed, does not occur, if we calculate the density matrix of a duster exactly without the perturbation method. By considering only a small cluster, being characteristic of the Bethe approxi· mation, the long wavelength spin waves, which are important at lower temperatures, are excluded, so that the magnetization of the sublattice is completely saturated at OOK in just the same way as in the Ising model. It is shown that, in the Bethe approximation, Curie point of antiferromagnet is higher than that of ferromagnet, for the same magnitude of I J I·.
138 citations
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TL;DR: In this paper, the percolation probability, mean cluster size and pair connectedness respectively with magnetization, susceptibility and pair correlation function in ferromagnetic Ising models were investigated.
Abstract: Rigorous inequalities are proved, which relate percolation probability, mean cluster size and pair connectedness respectively with magnetization, susceptibility and pair correlation function in ferromagnetic Ising models. In two dimensions the critical point is shown to be a percolation point, while in three dimensions this is not true.
138 citations