Aperiodic spin chain in the mean field approximation

Surface and bulk critical properties of an aperiodic spin chain are investigated in the framework of the phi(4) phenomenological Ginzburg-Landau theory. According to Luck's criterion, the mean field correlation length exponent nu = 1/2 leads to a marginal behaviour when the wandering exponent of the sequence is omega = -1. This is the case of the Fibonacci sequence that we consider here. We calculate the hulk and surface critical exponents for the magnetizations, critical isotherms, susceptibilities and specific heats. These exponents continuously vary with the amplitude of the perturbation. Hyperscaling relations are used in order to obtain an estimate of the upper critical dimension for this system.