Density fluctuations at critical points

Michael Ellis Fisher

I. S. Burmistrov, I. V. Gornyi, A. D. Mirlin

We review our recent theoretical results for mesoscopic fluctuations of the local density of states in the presence of electron–electron interaction. We focus on the two specific cases: (i) a vicinity of interacting critical point corresponding to an Anderson–Mott transition, and (ii) a vicinity of non-interacting critical point in the presence of a weak electron–electron attraction. In both cases, strong mesoscopic fluctuations of the local density of states exist.

А.З. Паташинский

Alan Martin Wolsky, M. S. Green, J. D. Gunton

The operator algebra and an identity in the statistical mechanics of fluids are used to demonstrate that the cumulant average of arbitrary products of appropriate combinations of local fluctuating energy and density are scale and conformal covariant at the critical point. These combinations are uncorrelated and are found by diagonalizing a matrix whose elements are energy and density derivatives of pressure-density and pressure-energy correlations. The eigenvalues are the dimensions of the appropriate variables.

Yu. L. Klimontovich

Kevin Ingersent, Qimiao Si A

Experiments in heavy-fermion metals and related theoretical work suggest that critical local-moment fluctuations can play an important role near a zero-temperature phase transition. We study such fluctuations at the quantum critical point of a Kondo impurity model in which the density of band states vanishes as /epsilon/(r) at the Fermi energy (epsilon=0). The local spin response is described by a set of critical exponents that vary continuously with r. For 0<r<1, the dynamical susceptibility at the critical point exhibits omega/T scaling with a fractional exponent, implying that the critical point is interacting.