Critical phenomena in semi-infinite systems. I.εexpansion for positive extrapolation length

The Wilson-Fisher expansion is used to calculate critical exponents to first order in =4-d for n-dimensional classical spins on a semi-infinite lattice with surface exchange such that the extrapolation length is positive. It is found that to first order in, all surface exponents can be calculated from bulk exponents and a single surface exponent, \~{}= (1{2) (n+2) } (n+8), describing the rate at which bulk correlation functions are approached when all coordinates are far from the surface. The exponents _ and _ introduced by Binder and Hohenberg are, respectively, 1- \~{} and 2 (1- \~{}). A form for the fixed-point spin correlation valid for all dimensions containing only the exponents and \~{} is proposed. With this form, all critical exponents for a semi-infinite system can be obtained from, , and \~{} if scaling is assumed.