Statistical Physics of Fields
While many scientists are familiar with fractals, fewer are familiar with scale-invariance and universality which underlie the ubiquity of their shapes. These properties may emerge from the collective behaviour of simple fundamental constituents, and are studied using statistical field theories. Initial chapters connect the particulate perspective developed in the companion volume, to the coarse grained statistical fields studied here. Based on lectures taught by Professor Kardar at MIT, this textbook demonstrates how such theories are formulated and studied. Perturbation theory, exact solutions, renormalization groups, and other tools are employed to demonstrate the emergence of scale invariance and universality, and the non-equilibrium dynamics of interfaces and directed paths in random media are discussed. Ideal for advanced graduate courses in statistical physics, it contains an integrated set of problems, with solutions to selected problems at the end of the book and a complete set available to lecturers at www.cambridge.org/9780521873413.
What people are saying - Write a review
We haven't found any reviews in the usual places.
Preface page ix
Directed paths in random media 209
Solutions to selected problems
appear approximation average behavior bonds calculate closed configurations connected Consider constant construct continuous contributions correction correlation function correlation length corresponding critical critical point decay depends described dimensions direction distribution diverges effective eigenvalue equation example expansion exponent expression factor field finite fixed point fluctuations Fourier free energy Gaussian given graphs Hamiltonian hence higher implies indicate integral interactions invariant Ising model lattice leads Lett limit loop low temperatures magnetization matrix method modes Note obtained original parameter particles partition function paths perturbation phase phase transition Phys positive possible probability problem random recursion relations renormalization saddle point scale Show similar singular solution space spins square steps symmetry temperature theory transformation transition variables vector walks weight zero