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Submitted on 1 Jan 1985
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HOPPING AND STATIC CORRELATIONS OF
HIGHER ORDER IN A LATTICE GAS
K. Froböse, J. Jäckle
To cite this version:
JOURNAL DE P H Y S I Q U E
Colloque C9, supplément au n012, Tome 46, décembre 1985 page C9-141
H O P P I N G AND S T A T I C CORRELATIONS OF H I G H E R ORDER I N A L A T T I C E GAS
K. Frobose and J . ~ a c k l e
FacuZty of Physics, University o f Konstanz, 0-7750 Constance, F.R. G.
Abstract
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In interacting lattice gases at intermediate concent- rations the hopping rate is determined by the static correlations of relatively high order among the neighbours of the diffusing particle. For a square lattice with nearest-neighbour exclusion the relevant correlation functions are studied by Monte Carlo simulation and analytically by an extended Bethe-Peierls cluster approximation. The results of both methods are in good agreement with each other and allow to test the accurary of approximation schemes for higher-order correlation functions such as Kirkwood's superposition approximation and the Gaussian factorization.Transport poperties of dense liquids are sensitive to features of short-range structural order which are only partly described by radi- al distribution functions. In simple liquids, for example, the.rate of processes causing viscous flow and atomic diffusion is closely related to the relative amount of order and randomness in the first coordina- tion shell of the liquid atoms. The connection between atomic trans- port and short-range atomic correlations is more easily studied for lattice-gas models than for models of real liquids. In this contribu- tion we report calculations of the average atomic jump rate for a simple model of an interacting lattice gas: atoms with extended hard- core repulsion between nearest-neighbour sites on a square lattice. For this model the effect of interactions on the average atomic jump rate is expressed by the static correlation function
C9-142 JOURNAL DE PHYSIQUE
be tested. It should be noted that in the mode1 a phase transition to an ordered state with antiferromagnetic order occurs at a concentra- tion c = 0.37 / 1 , 2 / . Here we are only interested in the properties of the disordered phase.
Fig.? shows the result of the Monte Carlo calculation (MC) for the reduced vacancy availability factor V/ (1-c) in comparison with three approximations. The result of the Bethe-Peierls cluster approximation
(BPI for the cluster shown in the insert is in rather satisfactory agreement with the numerical data even at the highest concentrations considered. The agreement obtained with the superposition approxima- tion (SA), on the other hand, is rather poor, although the large er- rors of the results for the three- and four-site correlation function, into which the expression for V can be decomposed, cancel to a large extent. The Gaussian factorization (G) of higherorder correlation functions, which results from treating the occupation numbers as Gaussian random variables as in the mean spherical approximation, givesbetter agreement at intermediate concentrations, but fails -al- ly for the higher concentrations c > 0.3.
Fig. 1
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Reduced vacancy availability factor in the disordered phase as a function of concentration: Result of Monte Carlo calculation (MC)in comparison with results for various approximations (see text). Insert: Cluster used in Bethe-Peierls approximation.
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