FRACTALS AT T=T-C DUE TO INSTANTONLIKE CONFIGURATIONS

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 fluctua tions of the order parameter at the critical point (T = T-c) we show t hat instantonlike configurations, corresponding to the minima of the e ffective action functional, build up clusters with fractal geometry ch aracterizing locally the critical fluctuations. The connection between the corresponding (local) fractal dimension and the critical exponent s is derived. Possible extension of the local geometry of the system t o a global picture is also discussed. [S0031-9007(98)07547-4].