by Walter F Wreszinski (Univ. São Paulo) & Silvio R A Salinas (Univ. São Paulo)

At present, existing literature on this subject matter can only be said to relate in minor areas to this work. Important concepts in statistical mechanics, such as frustration, localization, Lifshitz and Griffiths singularities, multicritical points, modulated phases, superselection sectors, spontaneous symmetry breaking and the Haldane phase, strange attractors and the Hausdorff dimension, and many others, are illustrated by exactly soluble lattice models. There are examples of simple lattice models which are shown to give rise to spectacular phase diagrams, with multicritical points and sequences of modulated phases. The models are chosen to enable a concise exposition as well as a connection with real physical systems (as dilute antiferromagnets, spin glasses and modulated magnets). A brief introduction to the properties of dynamical systems, an overview of conformal invariance and the Bethe Ansatz and a discussion of some general methods of statistical mechanics related to spontaneous symmetry breaking, are included in the appendices. A number of exercises are included in the text to help the comprehension of the most representative issues.

• Diluted Systems (including systems in random external fields and the Blume-Emery-Griffiths Model)
• Lattice Models with Competing Interactions (including the Bak-Bruinsma-Aubry model, the mean-field ANNNI model and spin models on a Cayley tree)
• Spin Glasses (order parameter, thermodynamic limit, replica method and models on a Cayley tree)
• Quantum Lattice Models with Competing Interactions (including an introduction to some aspects of the Hubbard model, helicoidal ground states of quantum spin chains, localization in a spin-boson model and Griffiths-Lifshitz singularities in a model of a disordered harmonic chain)