The Sherrington-Kirkpatrick Model (Springer Monographs in Mathematics)

📘 Book Details

• Author: Panchenko, Dmitry

• Publisher: Springer

• Language: English

• Edition: 2013 ed.

• ISBN: 9781461462880

• Pages: 156

• Cover: Hardcover

• Dimensions: 10.0 x 6.3 x 0.3 inches

📝 About the Book

The Sherrington-Kirkpatrick Model by Dmitry Panchenko offers a rigorous and elegant exploration of one of the most significant achievements in the study of disordered systems—the Parisi solution. Focused on the renowned Sherrington-Kirkpatrick (SK) model for spin glasses, this book delves into the core mathematical ideas that underpin the theory, including the landmark resolution of the Parisi ultrametricity conjecture and a concise proof of the Parisi formula for free energy.

Written in a clear, accessible style, this monograph is designed for graduate students and researchers with a background in probability theory. It requires no prior familiarity with spin glasses, making it an ideal entry point into a challenging yet profoundly impactful area of modern mathematics and theoretical physics.

Panchenko not only presents detailed mathematical proofs but also explains the intuition behind the results, offering readers deep insights into the structural and probabilistic foundations of complex systems. Topics such as Gaussian interpolation, concentration of measure, Poisson processes, and exchangeable arrays are woven into the analysis, illustrating their broader applicability beyond the SK model.

Praised by leading scholars and recognized as a valuable addition to the literature, The Sherrington-Kirkpatrick Model is a definitive reference for anyone working at the intersection of probability, statistical mechanics, and optimization theory.