Critical temperature shifts for finite slabs in the ε-expansion

The critical temperature T c (b) of a d-dimensional system with finite thickness b in one of its dimensions approaches its bulk limit as b to infinity according to T c ( infinity )-T c (b) varies as b - lambda . To first order in epsilon =4-d the shift exponent lambda is found to be given by lambda =2-((n+2)/(n+8)) epsilon +O( epsilon 2 ), and thus satisfies the scaling relation lambda = nu d -1 , where nu d is the correlation length exponent of the bulk system and n is the order parameter dimensionality.