Advanced Statistical Mechanics

What do magnets, turbulent flows, neural networks, and epidemics have in common? Statistical mechanics asks how collective behavior emerges from many interacting parts and why different systems can sometimes obey the same large-scale laws. We'll study the Ising model, symmetry breaking, mean-field and Landau theory, fluctuations and correlation functions, scaling, universality, numerical methods, statistical field theory, renormalization group. The course moves between exact calculations, controlled approximations, physical arguments, computation, asking which variables matter, which details can be discarded, what survives at larger scales. The goal is not only to solve particular models, but to learn to recognize structures that make complex systems tractable.