Spin glasses: statics and dynamics

Viac o knihe

Over the last decade, spin glass theory has evolved from a captivating area of theoretical physics into a flourishing subject within probability theory. This transformation has largely been driven by the mathematical insights gained from the “Parisi solution” of the Sherrington–Kirkpatrick mean field model, thanks to the contributions of Guerra, Talagrand, and others. Concurrently, new aspects and applications of these methods have emerged. The present volume compiles reviews and shorter articles from lecturers at a summer school on spin glasses held in July 2007 in Paris. These contributions range from pedagogical introductions to cutting-edge research, providing a comprehensive overview of the current state of the field from a mathematical perspective. The review by Bovier and Kurkova offers a concise introduction to mean field models, starting with the Curie–Weiss model and progressing to the Parisi solution of the Sherrington–Kirkpatrick model. Ben Arous and Kuptsov present a contemporary perspective on disordered systems through local energy statistics, highlighting various approaches to Hamiltonians of disordered systems and positioning the Random Energy model as a universal mechanism for certain rare events. Correlation identities serve as a crucial tool in the analysis of spin glasses.