A Modern Approach to Critical Phenomena
Cambridge University Press, 04.01.2007
Critical phenomena is one of the most exciting areas of modern physics. This 2007 book provides a thorough but economic introduction into the principles and techniques of the theory of critical phenomena and the renormalization group, from the perspective of modern condensed matter physics. Assuming basic knowledge of quantum and statistical mechanics, the book discusses phase transitions in magnets, superfluids, superconductors, and gauge field theories. Particular attention is given to topics such as gauge field fluctuations in superconductors, the Kosterlitz-Thouless transition, duality transformations, and quantum phase transitions - all of which are at the forefront of physics research. This book contains numerous problems of varying degrees of difficulty, with solutions. These problems provide readers with a wealth of material to test their understanding of the subject. It is ideal for graduate students and more experienced researchers in the fields of condensed matter physics, statistical physics, and many-body physics.
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ˆλ action in Eq anomalous dimension approximation assumed becomes Bose–Einstein condensation chemical potential coefﬁcients components compute conﬁguration correlation function correlation length correlation length exponent Coulomb critical behavior critical exponents critical region deﬁned determined diagram in Fig dimensional dimensionless dipoles diverges duality equation example fast modes ﬁnd finite ﬁnite temperature ﬁrst ﬁrst-order transition fixed point ﬂow ﬂuctuations Fourier free energy frozen lattice superconductor fugacity gauge ﬁeld Gaussian Ginzburg–Landau implies inﬁnite integral Ising model Kosterlitz–Thouless transition ln(fc low temperatures lowest order mean-ﬁeld theory order parameter ordered phase particles partition function perturbation theory phase diagram Problem quadratic quantum phase transition renormalization group rescaling sine-Gordon Solution speciﬁc heat superﬂuid density superﬂuid transition symmetry three dimensions ultraviolet cutoff universality class upper critical dimension vanishes variables vector potential vortex vortices wavevectors Wilson–Fisher ﬁxed point XY model yields zero