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We need to minimize the functional

with This is a Lagrange problem with On the coexistence line
gM''=aM+2dM
^{3} |
(6) |

Multiply (6) by *M*'. Then

To find *C* note that at we have

(7) |

(8) |

(9) |

In the bulk the energy per unit volume is

In the interface layer we have free energy per unit volume Additional free energy per unit volume Surface tension is surface energy per unit area, i.e. Change of variables: or, substituting and(10) |

What happens at ? Coefficient *a* tends to zero as
.

As we are closer to the critical point, the interface layer becomes thicker, and the surface tension drops. Since , correlation length diverges, and means that the difference between the phases disappears. The penalty for forming interface becomes lower, and fluctuations grow.

© 1997

Thu Oct 16 20:58:44 EDT 1997