Functional integral representation of Landau-Ginsburg theory with fluctuations

Massimo Blasone A, Petr Jizba B, L. A. Smaldone

Victor Nikolaevich Popov, Vladimir Sergeevich Yarunin

Moira L. Steyn‐Ross, Crispin W. Gardiner

We present a stochastic theory of the renormalization-group transformations of the time-dependent Ginzburg-Landau model, describing a system which exhibits the characteristics of a second-order phase transition. We eliminate a certain range of the Fourier components of the magnetic spin variables via a projection-operator method. This effectively changes the scale of the system and transforms the coupling constants. The procedure is shown to be equivalent to the integration over short-wavelength modes as in the renormalization-group transformation performed by Wilson and Kogut. This equivalence shows that the projection-operator method is a valid procedure for scaling critical systems, and in particular it indicates that the treatment of fluctuations is systematic. We suggest that such a method should also provide a straightforward approach to the dynamic renormalization group.

Viktor Nikolayevich Popov

Nabil Iqbal, Hong Liu, Márk Mezei

We consider several types of quantum critical phenomena from finite-density gauge-gravity duality which to different degrees lie outside the Landau-Ginsburg-Wilson paradigm. These include: (i) a ``bifurcating'' critical point, for which the order parameter remains gapped at the critical point, and thus is not driven by soft order parameter fluctuations. Rather it appears to be driven by ``confinement'' which arises when two fixed points annihilate and lose conformality. On the condensed side, there is an infinite tower of condensed states and the nonlinear response of the tower exhibits an infinite spiral structure; (ii) a ``hybridized'' critical point which can be described by a standard Landau-Ginsburg sector of order parameter fluctuations hybridized with a strongly coupled sector; (iii) a ``marginal'' critical point which is obtained by tuning the above two critical points to occur together and whose bosonic fluctuation spectrum coincides with that postulated to underly the ``Marginal Fermi Liquid'' description of the optimally doped cuprates.