Criticality and intermittency in the order parameter space

We consider a critical system at equilibrium in terms of a characteristic e xtensive quantity M = M(phi) where phi is the corresponding order parameter . The random averaging over the configurations contributing to the critical partition function is replaced by a deterministic dynamical averaging alon g trajectories of a suitable defined mop. At the critical point this map sh ows a remarkable consistency in describing characteristic properties of the system, like the fractal geometry of the critical clusters consisting from point-sets with a non-vanishing value of M. The 'critical' map turns out t o belong to the class of type I intermittent maps. Finally we obtain a rela tion of the isothermal critical exponent delta to the Liapunov exponent lam bda of the map. (C) 2000 Elsevier Science B.V. All rights reserved.