SURFACE CRITICAL EXPONENTS OF SELF-AVOIDING WALKS ON A SQUARE LATTICEWITH AN ADSORBING LINEAR BOUNDARY - A COMPUTER-SIMULATION STUDY

Using the scanning simulation method, we study a model of a single sel f-avoiding walk (SAW) terminally attached to an adsorbing impenetrable linear boundary on a square lattice; an interaction energy E (epsilon < 0) is defined between the ''surface'' and a step (bond) that lies o n the surface. SAW's of up to N = 260 steps are studied from samples g enerated with different values of the scanning parameter, b = 3 and 5. In most cases the different samples lead to the same results, which s uggests that they are statistically reliable. At the ordinary point (i nfinite temperature T) our result for the growth parameter, mu = 2.638 16+/-0.00002, is equal, within the error bars, to the best known esti mate of Enting and Guttmann [J. Phys. A 18, 1007 (1985)]. Also, our va lue gamma1 = 0.9551+/-0.0003 agrees very well with Cardy's value gamma 1 = 61/64 = 0.953..., obtained from conformal invariance [Nucl. Phys. B 240, 514 (1984)]. At the special point, we obtain independently the estimates gamma1 = 1.478+/-0.020 and gamma11 = 0.860+/-0.026 and, ther efore, also two independent estimates for mu that are found to be equa l and very close to the Enting-Guttmann value. These results for gamma 1 and gamma11 satisfy the Barber scaling relation. However, our adsorp tion critical temperature -epsilon/k(B)T = K* = 0.722+/-0.004 is larg er than estimates previously obtained by the transfer-matrix method. C orrespondingly, our result for the crossover exponent phi = 0.562+/-0. 020 is significantly larger than a theoretical value of Burkhardt, Eis enriegler, and Guim [Nucl. Phys. B 316, 559 (1989)], phi = 1/2.