Effects of aerogel-like disorder on the critical behavior of O(m)-vector models. Recent simulations and experimental evidence - Vasquez, C.; Paredes, R. (Condensed Matter Physics, 2006)
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 4He belongs. Experiments report
interesting changes of critical exponents for this transition, when superfluid 4He 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
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 ⁴He 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. Both experiments and simulations suggest a shift in critical exponents
to values closer to the SRC instead of those of the LRC fixed point.