Survival of short-range order in the Ising model on negatively curved surfaces

Diffuse elastic scattering of neutrons has been observed from a single crystal of deuterated ammonium bromide and is interpreted as being due to short-range order among ammonium ion orientations. Both the temperature dependence of the diffuse intensity and its distribution in reciprocal space can be described in terms of a simple Ising model of the order-disorder transition. An expression for the diffuse intensity obtained from the mean-field approximation to the Ising model is least-squares fitted to the data. Interactions between first, second and third nearest neighbour ammonium ions have to be included in the model to give an adequate fit. The interaction energies so obtained are compared with calculations based on a simple electrostatic theory, For agreement, a charge of 0.358e on hydrogen atoms and a polarizability of 1.40 Å3 for Br− ions have to be assumed in the calculations and the significance of these unlikely values is discussed.

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Short range order and the magnetic properties of the binary alloys in the ising model

physica status solidi (b) ◽

10.1002/pssb.2221070141 ◽

1981 ◽

Vol 107 (1) ◽

pp. K1-K4 ◽

Cited By ~ 2

Author(s):

A. Z. Maksymowicz ◽

W. Karaś

Keyword(s):

Magnetic Properties ◽

Ising Model ◽

Short Range ◽

Short Range Order ◽

Binary Alloys ◽

Range Order

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Correlation Function Approach to Short-Range Order in the Ising-Model

Zeitschrift für Naturforschung A ◽

10.1515/zna-1970-0206 ◽

1970 ◽

Vol 25 (2) ◽

pp. 181-188

Author(s):

Rainer J. Jelitto

Keyword(s):

Correlation Function ◽

Ising Model ◽

Short Range ◽

Short Range Order ◽

Slight Modification ◽

Natural Generalization ◽

Range Order ◽

Model Variant ◽

Point Correlation ◽

Point Correlation Function

Abstract By pushing forward the decoupling from the three-to the four-point correlation function short-range order is systematically introduced into the description of the statistical behaviour of the Ising-model. Application of a procedure which is a natural generalization of that invented by Bogoljubov and Tjablikov for the Heisenberg-model, leads to an overall-approximation for the magnetization and the nearest-neighbour correlation which may be compared with the Ising-model variant of Oguchi's two-spin-cluster molecular field theory. The results of both approximations are very similar both for low and high temperatures, but for the transition point the new approach yields values which lie considerably lower and therefore are more reliable than those following from Oguchi's theory. Moreover, the comparison with a slight modification of the theory which is also presented in this paper, illuminates the physical mechanism which is responsible for the formation of correlations within the order of approximation, considered.

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