Statistical Mechanics

<p>This textbook is based on lecture notes that the author delivered at Qiuzhen College (Tsinghua University) a Chinese institution known for its exceptionally talented mathematics students. The book's intended audience shapes its character. It introduces Statistical Mechanics from the ground up offering a fully self-contained presentation that aims for mathematical precision. It distinguishes rigorous results from controlled approximations and provides physical insights into phenomena.</p><p>Despite its concise nature (suited for a one-semester basic course) this book covers several topics typically not found in introductory texts. These include Shannon's information-theoretic interpretation of entropy the gauge approach to order-disorder duality in the Ising model the Yang-Lee theory and the quantum dissipation-fluctuation theorem. Additionally it explores frustrated and quenched systems including an introduction to the celebrated Parisi solution of the Sherrington-Kirkpatrick model of spin glasses.</p><p>The path integral formalism is extensively discussed from various perspectives to suit different applications. Chapter 2 approaches path integrals through the Feynman-Kac formula and second quantization. In Chapter 5 they are examined within the context of effective field theories like Landau-Ginzburg theory while Chapter 6 delves into their connection with Brownian motion Langevin stochastic differential equations and Fokker-Planck diffusion PDEs. The book also explores the relationship between stochastic processes and supersymmetry.</p><p>Various techniques for computing path integrals especially functional determinants are introduced throughout the relevant chapters offering the most suitable computational tools for each application.</p>