Effects of aerogel-like disorder on the critical behavior of O(m)-vector models. Recent simulations and experimental evidence

Abstract

We review recent results on the effect of a specific type of quenched disorder on well known O(m)-vector models in three dimensions: the XY model (3DXY, m = 2) and the Ising model (3DIS, m = 1). Evidence of changes of criticality in both systems, when confined in aerogel pores, is briefly referenced. The 3DXY model represents the universality class to which the λ-transition of bulk superfluid 4 He belongs. Experiments report interesting changes of critical exponents for this transition, when superfluid 4 He is confined in aerogels. Numerical evidence has also been presented that the 3DXY model, confined in aerogel-like structures, exhibits critical exponents different from those of bulk, in agreement with experiments. Both results seem to contradict Harris criterion: being the specific heat exponent negative for the pure system (α 3DXY −0.011 < 0), changes should be explained in terms of the extended criterion due to Weinrib and Halperin, which requires disorder to be long-range correlated (LRC) at all scales. In numerical works, aerogels are simulated by the diffusion limited cluster-cluster aggregation (DLCA) algorithm, known to mimic the geometric features of aerogels. These objects, real or simulated, are fractal through some decades only, and present crossovers to homogeneous regimes at finite scales, so the violation to Harris criterion persists. The apparent violation has been explained in terms of hidden LRC subsets within aerogels [Phys. Rev. Lett., 2003, 90, 170602]. On the other hand, experiments on the liquid-vapor (LV) transition of 4 He and N 2 confined in aerogels, also showed changes in critical-point exponents. Being the LV critical-point in the O(1) universality class, criticality may be affected by both short-range correlated (SRC) and LRC subsets of disorder. Simulations of the 3DIS in DLCA aerogels can corroborate experimental results. Both experiments and simulations suggest a shift in critical exponents to values closer to the SRC instead of those of the LRC fixed point.

Superfluid hydrodynamic in fractal dimension space

“…do not change the intertial reference frame. As a consequence there is some special reference frame where the fractional Schrödinger equation has form (5). One can identify this reference frame with some reference frame where, for example, nanoporous media is in a rest.…”

“…The question of influence of geometrical factors (confinement dimension, dimension of nanopores space, etc) has been emerged [1,2,3,4,5,6]. So one has to apply a new physics to describe such systems with taking into account their complex nature.…”

Quantum fluids in nanoporous media—Effects of the confinement and fractal geometry

“…Also it has been demonstrated [7] that it is long-correlated structure of aerogel that makes an essential influence on liquid 4 He behavior near λ-point.…”