Tricritical behavior and polymer adsorption at dirty surfaces or walls

Nuclear Physms B (Proc. Suppl ) 5A (1988) 185 North-Holland, A m s t e r d a m

185

TRICRITICAL

B E H A V I O R AND P O L Y M E R A D S O R P T I O N

H.

and

W. D I E H L

A.

Fachbereich Physik, West Germany

AT D I R T Y S U R F A C E S

OR W A L L S

NOSSER UniversitNt

Essen

GHS,

Postfach

103

764,

D-4300

Essen

1,

We s t u d y the effects of weak quenched disorder that is present only at the surface of macroscopic systems on their surface critical behavior at a bulk trlcritical point. To this end a recent detailed renormalization-group t of a semi-inifinite continuum model of the O(n) type with a 1016 bulk nonlinearity and a 1014 s u r f a c e nonlinearity is generalized to include a randomly fluctuating quadratic surface interaction (randomly fluctuating surface enhancement). For n=O, the model describes the adsorption of linear polymers in a there solvent, at a dirty wall. Field-theoretic methods are used in conjunction with the replica trick to investigate the model for space dimensionalities d=3-e ~ d~=3, the upper critical dimension. Just as in the pure case, the surface critical exponents at the special transition have an expansion in ~e for e > 0, and logarithmic corrections of a non-power-law form appear for d=3. We f i n d that the kind of surface disorder considered is irrelevant for d=3 and for sufficiently small e > O. T h i s is in conformity with a criterion of the Harris type saying that disorder is irrelevant if d-1 < 2~/u = 211 - a(n)~e + O(e)], where 0 is the surface crossover exponent at the infrared-stable pure fixed point.

REFERENCES 1.

H W. Diehl and E. Eisenriegler, Europhys Lett. 4 (1987) 709; E. Eisenriegler and H. W. D i e h l , Phys. Rev. B, to appear.

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