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Conformal Invariance and Critical Phenomena (Paperback, Softcover reprint of hardcover 1st ed. 1999)
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Conformal Invariance and Critical Phenomena (Paperback, Softcover reprint of hardcover 1st ed. 1999)
Series: Theoretical and Mathematical Physics
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Critical phenomena arise in a wide variety of physical systems.
Classi cal examples are the liquid-vapour critical point or the
paramagnetic ferromagnetic transition. Further examples include
multicomponent fluids and alloys, superfluids, superconductors,
polymers and fully developed tur bulence and may even extend to the
quark-gluon plasma and the early uni verse as a whole. Early
theoretical investigators tried to reduce the problem to a very
small number of degrees of freedom, such as the van der Waals
equation and mean field approximations, culminating in Landau's
general theory of critical phenomena. Nowadays, it is understood
that the common ground for all these phenomena lies in the presence
of strong fluctuations of infinitely many coupled variables. This
was made explicit first through the exact solution of the
two-dimensional Ising model by Onsager. Systematic subsequent
developments have been leading to the scaling theories of critical
phenomena and the renormalization group which allow a precise
description of the close neighborhood of the critical point, often
in good agreement with experiments. In contrast to the general
understanding a century ago, the presence of fluctuations on all
length scales at a critical point is emphasized today. This can be
briefly summarized by saying that at a critical point a system is
scale invariant. In addition, conformal invaTiance permits also a
non-uniform, local rescal ing, provided only that angles remain
unchanged."
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