CROSS-OVER AND EFFECTIVE SCALING DIMENSIONS

Abstract

Although cross over between fixed points associated with different universality classes is a ubiquitious phenomena, there is little theoretical insight and less numerical evidence about exactly how cross-over phenomena occur. Here numerical evidence for the picture that cross-over phenomena are governed by the underlying structure of the associated renormalization group is given. In particular, it is shown how the cross-over is related to the effective dimension from scaling of the system. For the ferromagnetic Ising model in two and three dimensions numerical evidence will be presented that the cross-over is governed by the line of fixed points in non-integer dimensions. This allows for successful comparisons between the effective dimension from scaling for finite systems and expansions in dimension of universal quantities such as critical exponents.