# Low-Temperature Analysis of Microemulsion Model

Chapter

## Abstract

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: where φ(

$$H(\varphi ({\mathbb{Z}^3})) = - I\sum\limits_{dist(x,y) = 1} {\varphi (x)\varphi (y) - J\sum\limits_{dist(x,y) = \sqrt 2 } {\varphi (x)\varphi (y) - K\sum\limits_{dist(x,y) = 2} {\varphi (x)\varphi (y)} } }$$

(1)

*ℤ*^{3}) is a configuration on*ℤ*^{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.## Keywords

State Diagram Mixture Parameter Mathematical Geophysics Periodic Ground Periodic Configuration
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## References

- 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