Field-theoretical approach to multicritical behavior near free surfaces

Abstract

The critical behavior of a semi-infinite $n$-vector model in $4\ensuremath{-}\ensuremath{\epsilon}$ dimensions near the special transition is studied. The renormalization of the relevant surface operators is discussed and explicitly carried out in two-loop order. It is found that the crossover exponent ${\ensuremath{\varphi}}_{s}$ related to the square of the order parameter in the surface does not satisfy the relation ${\ensuremath{\varphi}}_{s}=1\ensuremath{-}\ensuremath{\nu}$ due to Bray and Moore.