6533b7d4fe1ef96bd1261c79

RESEARCH PRODUCT

Effects of surface nonlinear interactions on the local critical behavior

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Effects of surface nonlinear interactions on the local critical behaviors are studied for an-component field in the semi-infinite space near the SB (surface-bulk) point by using renormalization group methods. The model Hamiltonian consists of a free (Gaussian) bulk part and a surface term containing aφ4 interaction. The interplay between the free bulk term and the nonlinear surface term gives rise to interesting behaviors of the local surface properties. Whereas the local susceptibility and correlation exponents retain their mean-field values, the surface crossover exponent ϕ is non-mean-field below three dimensions. To second order in e(e=3−d) we find:η‖ and\(\phi = \frac{1}{2} - \frac{{n + 2}}{{2(n + 8)}}\varepsilon - \frac{{2(n + 2)(7n + 20)\ln 2}}{{(n + 8)^3 }}\varepsilon ^2\). The fact that (1−ϕ)/ν>1 in this model indicates that at the SB point the surface is effectively repulsive, in contrast to the widely-studied semi-infinite-spaceφ4 model. Logarithmic corrections are obtained at the upper critical dimensiond=3. Interesting comparisons are made of the results for this model with those for the semi-infinite-spaceφ4 model as well as for the tricriticalφ6 model. Applications to the adsorption of polymers (then→0 limit) are discussed in conjunction with a recent Monte Carlo simulation by van Dieren and Kremer.