Almeida-Thouless transition below six dimensions

Abstract

The existence of an Almeida-Thouless (AT) instability surface below the upper critical dimension 6 is demonstrated in the generic replica symmetric field theory. Renormalization flows from around the zero-field fixed point are investigated. By introducing the temperature and magnetic field dependence of the bare parameters, the fate of the AT line can be followed from mean field (infinite dimensions) down to d<6.