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In recent years a lot of interest has been raised by quantum phase
transitions involving a smooth disappearance of a Fermi-surface. As one
approaches such critical points, the Landau-quasiparticle weight and
velocity tend to zero, nevertheless, the Fermi surface remains sharply
defined. One proposed example of such a transition is the development of
Ising-nematic order in a metal. This order, associated with electronic
correlations, which spontaneously break the square lattice symmetry to
that of a rectangular lattice, has been observed in the enigmatic normal
state of the cuprate superconductors by a number of recent experiments.
Motivated by these findings, I will present the scaling theory of the
Ising-nematic transition in a two-dimensional metal. The critical point
is described by an infinite set of 2+1 dimensional local field theories,
labeled by points on the Fermi surface. Scaling forms for the response
functions are proposed, and supported by computations up to three loops.
Our results extend also to the theory of a Fermi surface coupled to a
U(1) gauge field, which describes a number of spin and charge-liquid
states.
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