Fractals at T=Tc due to instanton-like configurations

Abstract

We investigate the geometry of the critical fluctuations for a general system undergoing a thermal second order phase transition. Adopting a generalized effective action for the local description of the fluctuations of the order parameter at the critical point ($T=T_c$) we show that instanton-like configurations, corresponding to the minima of the effective action functional, build up clusters with fractal geometry characterizing locally the critical fluctuations. The connection between the corresponding (local) fractal dimension and the critical exponents is derived. Possible extension of the local geometry of the system to a global picture is also discussed.