Disorder and Competition in Soluble Lattice ModelsWorld Scientific, 1993 - 236 страница 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. |
Садржај
General Introduction | 1 |
Lattice Models with Competing Interactions | 41 |
Spin Glasses | 93 |
Quantum Lattice Models with Competing Interactions | 131 |
A A Brief Introduction to Dynamical Systems | 177 |
B The Theorems of Aubry | 199 |
Bethe Ansatz and Conformal Invariance | 205 |
Unicity of Phases Unicity in a Sector and Spontaneous Symmetry | 223 |
231 | |
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Disorder and Competition in Soluble Lattice Models Walter F Wreszinski,Silvio R A Salinas Ограничен приказ - 1993 |
Чести термини и фразе
ANNNI model antiferromagnet Appendix associated attractor Aubry behavior Bethe Ansatz Cayley tree Chapter classical competing interactions configuration conformal invariance consider contours corresponding critical defined devil's staircase dimension discuss distribution E.H.Lieb eigenvalues equation ergodic example existence external field ferromagnetic finite fixed point free energy given by Eq ground H₁ Hamiltonian Heisenberg Hemmen Hence Hubbard model infinite integer Ising model J₁ lattice models Lett Lifshitz linear Lyapunov exponent magnetization Math matrix mean-field N.York Néel obtain one-dimensional order parameter paramagnetic periodic boundary conditions phase diagram phase transition Phys physical potential probability problem quantum random variables random-field replica Section SK model solution spin spin-glass stable Stat statistical mechanics structure symmetry tanh temperatures theorem theory thermodynamic limit tricritical tricritical point values vector write XXZ chain zero field ән