Effects of aerogel - like disorder on the critical behavior of O ( m ) – vector models . Recent

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). Evidences of changes of criticality in both systems, when confined in aerogel pores, are briefly referenced. The 3DXY model represents the universality class to which the λ–transition of bulk superfluid He belongs. Experiments report interesting changes of critical exponents for this transition, when superfluid 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 (α3DXY ≃ −0.011 < 0), changes must 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 He and N2 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. Experiments and simulations both suggest a shift in critical exponents to values closer to the SRC instead of those of the LRC fixed point.