PHASE TRANSITIONS ABOVE THE UPPER CRITICAL DIMENSION

Bertrand Berche (Personal webpage)

We revisit the very smart scenario proposed by M.E. Fisher in the eighties to explain the mismatch between Landau exponents in the mean field theory and the Gaussian fixed point RG eigenvalues above the upper critical dimension. This scenario (the dangerous irrelevant variable) has been improved further to explain some discrepancies which still spoil the whole scaling picture when finite-size scaling is considered. We will present some old and recent results in the case of O(n) models and will fly over extensions to other universality classes.