Multiple crossover phenomena and scale hopping in two dimensions

We study the renormalization group for nearly marginal perturbations of a minimal conformal field theory M_p with p 1. To leading order in perturbation theory, we find a unique one-parameter family of “hopping trajectories” that is characterized by a staircase-like renormalization group flow of the C-function and the anomalous dimensions and that is related to a factorizable scattering theory recently solved by Al. B. Zamolodchikov. We argue that this system is described by interactions of the form . As a function of the relevant parameter t, it undergoes a phase transition with new critical exponents simultaneously governed by all fixed points M_p, M_p−1,…, M₃. Integrable lattice models represent different phases of the same integrable system that are distinguished by the sign of the irrelevant parameter .