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Unbinding transitions of amphiphilic membranes are studied by a renormalization group (RG) approach. Both for fluid and for crystalline membranes, a whole line of RG fixed points is found. Each line consists of two branches: one branch describes complete unbinding, the other branch represents continuous unbinding transitions. The critical behaviour at the unbinding transition exhibits three scaling regimes A ), B ), and C ). Regime A ) is characterized by essential singularities, and regime B ) by parameter-dependent critical exponents. In regime C ), a discontinuous transition with rather unusual scaling properties is expected by analogy with wetting transitions.
There are two types of interaction between membranes - direct interaction and fluctuations. These involve several length scale - so DI is renormalized by FL and might change sign with change of FL. In liquid membranes the rigidity, K, is constant and FL energy is K(del^2 l(x))^2. For gel phase, Keff goes like K/q^eta where eta is between 1 and 2/3. So eta=0 for fluid membrane.
The Hamiltonian is a surface integral of : 1/2 K q^(4-eta) l(q)^2 + P*l(x) + DI(l(x)).
The math is quite complicated but it tells of an unbinding transition at low T.
The author refers allot to two references - 4 and 5 - in order to fully understand this.
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