Competition between singlet formation and magnetic ordering in one-dimensional spin systems

We use mappings onto soluble models and Abelian bosonization to determine the phase diagram and correlation functions of a model of two coupled spin chains. We find quantum disordered singlet phases and magnetic phases and determine the phase boundaries, universality classes of transitions, and correlation functions. We believe our model captures the essential physics of the interplay between the Kondo effect and magnetic ordering, which may be important for the heavy fermion materials.