Low-Temperature Analysis of Microemulsion Model

  • A. E. Mazel
Part of the NATO ASI Series book series (NSSB, volume 264)


The microemulsion model was proposed by B.Widom for the description of the microfilm structure in the “oil-water” mixture with some values of the mixture parameters. The model is a classical 3-D spin lattice model. The spin takes the values ±1 and the interaction is described by the Hamiltonian:
$$H(\varphi ({\mathbb{Z}^3})) = - I\sum\limits_{dist(x,y) = 1} {\varphi (x)\varphi (y) - J\sum\limits_{dist(x,y) = \sqrt 2 } {\varphi (x)\varphi (y) - K\sum\limits_{dist(x,y) = 2} {\varphi (x)\varphi (y)} } }$$
where φ( 3) is a configuration on 3, x,y∈ℤ 3, J=-2K. This Hamiltonian includes the interaction of nearest neighbours in the first sum, the interaction of diagonal neighbours in the second sum and the interaction of next nearest neighbours in the third sum.


State Diagram Mixture Parameter Mathematical Geophysics Periodic Ground Periodic Configuration 
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  1. 1.
    E.I. Dinaburg and A.E. Mase’, Analysis of Low-Temperature Phase Diagram of Microemulsion Model, Commun. Math. Phys., V. 125:27 (1989).ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1991

Authors and Affiliations

  • A. E. Mazel
    • 1
  1. 1.International Institute of Earthquake Prediction Theory and Mathematical GeophysicsAcademy of SciencesMoscowUSSR

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