Multiple Crossover Phenomena and Scale Hopping in Two Dimensions

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We study the renormalization group for nearly marginal perturbations of a minimal conformal field theory Mₚ 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 recently solved factorizable scattering theory. We argue that this system is described by interactions of the form t phi₍₁,₃₎ - t' ϕ₍₃,₁₎. As a function of the relevant parameter t, it undergoes a phase transition with new critical exponents simultaneously governed by all fixed points Mₚ, Mₚ₋₁,..., M₃. Integrable lattice models represent different phases of the same integrable system that are distinguished by the sign of the irrelevant parameter t'.