Condensed Matter Physics

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

Vásquez, Ricardo Paredes V.

Published Jan 1, 2006• 5 citations

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.

DOI: 10.5488/cmp.9.2.305

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Condensed Matter Physics

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

Vásquez, Ricardo Paredes V.

Published Jan 1, 2006• 5 citations

Publisher

Abstract

DOI: 10.5488/cmp.9.2.305

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\lambda

-transition in

^{4}

He. This has qualitative implications on expected experimental signatures in a defect supersolid scenario.For the Bose glass to superfluid quantum phase transition in 2D we determine the quantum correlation time by an anisotropic finite size scaling approach. Without a priori assumptions on critical parameters, we find the critical exponent

z=1.8 \pm 0.05

contradicting the long standing result

z=d

.Using a 3D effective model for multi-band type-1.5 superconductors we find that these systems possibly feature a strong first order vortex-driven phase transition. Despite its short-range nature details of the interaction are shown to play an important role.Phase transitions in disordered spin models exposed to correlated defect structures obtained via rapid quenches of critical loop and spin models are investigated. On long length scales the correlations are shown to decay algebraically. The decay exponents are expressed through known critical exponents of the disorder generating models. For cases where the disorder correlations imply the existence of a new long-range-disorder fixed point we determine the critical exponents of the disordered systems via finite size scaling methods of Monte Carlo data and find good agreement with theoretical expectations.

\lambda

-transition in

^{4}

z=1.8 \pm 0.05

contradicting the long standing result

z=d

\alpha

. According to the Harris criterion disorder should hence lead to a new fixed point characterized by new critical exponents. We have determined the phase diagram of the diluted model, starting from the pure model limit down to the neighbourhood of the percolation threshold. For the estimation of critical exponents, we have first performed a finite-size scaling study, where we concentrated on three different dilutions to check the stability of the disorder fixed point. We emphasize in this work the great influence of the cross-over phenomena between the pure, disorder and percolation fixed points which lead to effective critical exponents dependent on the concentration. In a second set of simulations, the temperature behaviour of physical quantities has been studied in order to characterize the disorder fixed point more accurately. In particular this allowed us to estimate ratios of some critical amplitudes. In accord with previous observations for other models this provides stronger evidence for the existence of the disorder fixed point since the amplitude ratios are more sensitive to the universality class than the critical exponents. Moreover, the question of non-self-averaging at the disorder fixed point is investigated and compared with recent results for the bond-diluted q = 4 Potts model. Overall our numerical results provide evidence that, as expected on theoretical grounds, the critical behaviour of the bond-diluted model is indeed governed by the same universality class as the site-diluted model.

x

. We extend the Harris criterion for this case, finding that for

a<d

(where

d

is the spatial dimension) the disorder is irrelevant if $a\ensuremath{\nu}\ensuremath{-}2>0$, while if

a>d

we recover the usual Harris criterion: The disorder is irrelevant if $d\ensuremath{\nu}\ensuremath{-}2=\ensuremath{-}\ensuremath{\alpha}>0$. An

m

-vector system of this type is studied with the use of a renormalization-group expansion in $\ensuremath{\epsilon}=4\ensuremath{-}d$ and $\ensuremath{\delta}=4\ensuremath{-}a$. We find a new long-range-disorder fixed point in addition to the short-range-disorder and pure fixed points found previously. The crossover between fixed points is found to follow the extended Harris criterion. The new fixed point has complex eigenvalues, leading to oscillating corrections to scaling, and has a correlation-length exponent $\ensuremath{\nu}=\frac{2}{a}$. We argue that this new scaling relation is exact and applies more generally than just to the specific model. We show that the extended Harris criterion also applies to percolation with long-range-correlated site or bond-occupation probabilities, so that the scaling law should be obeyed by such systems. Results for the percolation properties of the triangular Ising model are in agreement with these predictions.