Second-order phase transition in crystals with long-range correlated quenched defects

Korzhenevskii, A. L.; Herrmanns, K.; Schirmacher, Walter

doi:10.1103/physrevb.53.14834

Cited by 15 publications

(30 citation statements)

References 22 publications

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“…On the other hand, many experimental contributions in the last two decades posed interesting questions about criteria of relevance, supplying results that challenge predictions made by previous theoretical works. Amongst all, those on the superfluid transition of 4 He in light aerogels are rather intriguing [6][7][8][9][10][11]. Changes of critical exponents for the so called λ-transition, when superfluid 4 He is confined in aerogel pores, were reported repeatedly from late 80's through late 90's, with almost the same question left open: do these results violate Harris and/or other relevance criteria?…”

Section: Harris Criterion In Brief: Original and Extendedmentioning

confidence: 87%

“…The challenge to theory comes in the case of 4 He confined in silica aerogels (AE) and xerogels (XE), where authors observed ζ AE 0.81 and ζ XE 0.89, respectively, larger than the bulk exponent. After the WH model, these results suggest that LRC distributions of defects should be present within AE and XE.…”

Section: Phase Transitions In Aerogels: Experimentsmentioning

confidence: 99%

“…In terms of the WH model, this 4 He-Vycor system falls into the SRC regime (1), so theoretical predictions agree with experiments. Alternatively, Zassenhaus and Reppy [20], reported calorimetric studies for this 4 He-Vycor system, showing that the singular part of specific heat curves fit well a λ-like curve with the same exponent α as bulk SF 4 He. Further experiments, using porous gold to confine SF 4 He, instead of Vycor, confirm these results [21].…”

Section: Phase Transitions In Aerogels: Experimentsmentioning

confidence: 99%

“…The question arises because aerogels are homogeneous (non-correlated) beyond a finite scale [12,13], and given that the specific heat exponent (α) is negative for this transition, exponents should not change after Harris criterion. Many numerical and theoretical works have since emerged to explain these contradictory results [4,5,[14][15][16][17].…”

Section: Harris Criterion In Brief: Original and Extendedmentioning

confidence: 99%

“…In 1988, Moses Chan et al [6] reported on the effect of quenched disorder on the superfluid (SF) transition of confined 4 He, using three types of porous glass: Vycor, aerogels and xerogels. They measured the temperature dependence of the relative superfluid density, which scales as ρ s /ρ ∼ t ζ near the critical point, being t = |T − T c |/T c the reduced temperature, and the exponent ζ ≡ ν due to hyperuniversality [9,11].…”

Section: Phase Transitions In Aerogels: Experimentsmentioning

confidence: 99%

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

Vásquez¹,

Paredes²

2006

Condens. Matter Phys.

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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.

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Section: Harris Criterion In Brief: Original and Extendedmentioning

confidence: 87%

Section: Phase Transitions In Aerogels: Experimentsmentioning

confidence: 99%

Section: Phase Transitions In Aerogels: Experimentsmentioning

confidence: 99%

Section: Harris Criterion In Brief: Original and Extendedmentioning

confidence: 99%

Section: Phase Transitions In Aerogels: Experimentsmentioning

confidence: 99%

See 3 more Smart Citations

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

Vásquez¹,

Paredes²

2006

Condens. Matter Phys.

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Percolation in networks with long-range connections

Moukarzel

2006

Physica A: Statistical Mechanics and its Applications

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On the universality class of the 3d Ising model with long-range-correlated disorder

Ivaneyko

Berche²,

Holovatch

et al. 2008

Physica A: Statistical Mechanics and its Applications

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We analyze a controversial topic about the universality class of the three-dimensional Ising model with long-range-correlated disorder. Whereas both theoretical and numerical studies agree on the validity of extended Harris criterion (A. Weinrib, B.I. Halperin, Phys. Rev. B 27 (1983) 413) and indicate the existence of a new universality class, the numerical values of the critical exponents found so far differ essentially. To resolve this discrepancy we perform extensive Monte Carlo simulations of a 3d Ising model with non-magnetic impurities being arranged in a form of lines along randomly chosen axes of a lattice. The Swendsen-Wang algorithm is used alongside with a histogram reweighting technique and the finite-size scaling analysis to evaluate the values of critical exponents governing the magnetic phase transition. Our estimates for these exponents differ from both previous numerical simulations and are in favour of a non-trivial dependency of the critical exponents on the peculiarities of long-range correlations decay.

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Second-order phase transition in crystals with long-range correlated quenched defects

Abstract: We consider the phase transition in a ferromagnet with line defects that

Cited by 15 publications

References 22 publications

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

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

Percolation in networks with long-range connections

On the universality class of the 3d Ising model with long-range-correlated disorder

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