Comment on “Order parameter fluctuations at the critical point”

A. Widom

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.

Heiner Muller-Krumbhaar, K. A. Müller

João Amaro de Matos, J. A. Baêta Segundo, J F Perez

The authors compute the fluctuations of the order parameter in the Curie-Weiss version of a site-dilute antiferromagnet. Their results show: (i) Gaussian fluctuations away from criticality or at a first-order critical point with sample and thermal fluctuations contributing in same order; (ii) Non-Gaussian fluctuations with critical exponents modified by the presence of dilution at the second-order critical point. In this case sample-induced fluctuations are enhanced to dominate over the thermal ones. Critical exponents are the same as in the Curie-Weiss random field Ising model.

Michael Ellis Fisher

六美 水戸部, Kousuke Yakubo

General form of the probability distribution function (PDF) of the rescaled fractal dimension characterizing spatial structures of local order parameters in finite but large systems near the critical point is derived. To obtain the PDF, we assume that (i) sample-to-sample fluctuations of global order parameters are described by the generalized Gumbel distribution function, which is known to be valid for many of long-range correlated systems such as critical systems and (ii) spatial structures of local order parameters are always fractal at the critical point. From the obtained PDF, it is elucidated that fluctuations of fractal dimensions do not exhibit a universal character in contrast to the case of fluctuating global order parameters. In addition, we perform numerical calculations of the PDF for two-dimensional percolation systems near the critical concentration and confirm that the analytically calculated PDF well describes numerical results. We also discuss the influence of non-fractal critical clusters neglected under the assumption (ii).