Strong disorder RG approach – a short review of recent developments

Iglói, Ferenc; Monthus, Cécile

doi:10.1140/epjb/e2018-90434-8

Cited by 84 publications

(76 citation statements)

References 303 publications

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“…To treat these correlations quantitatively, in Sec. IV we use a version of Strong-Disorder Renormalization Group (SDRG), originally due to D. S. Fisher [17,18], and extensively reviewed in [19][20][21]. We find our problem to be formally similar to the one studied in Ref.…”

Section: Introductionmentioning

confidence: 99%

Strange metal state near quantum superconductor-metal transition in thin films

Tikhonov

Фейгельман

2020

Annals of Physics

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We develop a theory of quantum T = 0 phase transition (q-SMT) between metal and superconducting ground states in a two-dimensional metal with frozen-in spatial fluctuations δλ(r) of the Cooper attraction constant. When strength of fluctuations δλ(r) exceeds some critical magnitude, usual mean-field-like scenario of the q-SMT breaks down due to spontaneous formation of local droplets of superconducting phase. The density of these droplets grows exponentially with the increase of average attraction constant λ. Interaction between the droplet's order parameters is due to proximity effect via normal metal and scales with distance ∝ 1/r β , with 2 < β ≤ 3. We account for this interaction by means of a real-space strong-disorder renormalization group (RG). Near the q-SMT the RG flow is, formally, a dual equivalent of the Kosterlitz-Thouless RG. The corresponding line of fixed points describes a Griffiths phase of a metal with large fractal clusters of superconducting islands. Typical number of islands in a cluster grows as N δ ∼ 1/δ, where 0 < δ 1 is the distance to the critical point. Superconducting side is described by a runaway of RG trajectories into the strong-coupling region. Close to the transition point on the SC side, 0 < −δ 1, RG trajectories possess an extremum as function of the RG parameter |δ| 1/2 ln(1/T τ ). It results in a wide temperature range where physical properties are nearly T -independent. This observation may be relevant to the understanding of a strange metal state frequently observed near q-SMT.PACS numbers:

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Section: Introductionmentioning

confidence: 99%

Strange metal state near quantum superconductor-metal transition in thin films

Tikhonov

Фейгельман

2020

Annals of Physics

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“…Our fits extrapolated to L → ∞ are shown as solid lines in Fig. 10(a) and are numerically equal to ζ x = 0.65(5), ζ z = 1.1 (2), δ x = 0.64(3), δ z = 0.62 (2), γ x = 1.71(3), γ z = 2.11 (5), b x = 4.6(3), b z = 8.7 (5), γ ′ x = 0.41 (3), and γ ′ z = 0.19 (2). We now step forward and study how P α depends on D. In Figs.…”

Section: Iii2 Typical Correlation Function and Probability Distribumentioning

confidence: 95%

“…Finally, given that the SDRG method is believed to provide exact results concerning the critical singularities of the model 1, it is desirable to investigate large system sizes in order to check the logarithmic corrections mentioned in Eqs. (4) and (5). The motivation for searching these logarithmic corrections to (3) is justified in the early works of homogeneous XXZ spin-1/2 chains [25-27, 29-31, 45], and also in a recent work of the random XXZ model [13].…”

Section: Ii4 Methods and Further Motivationsmentioning

confidence: 99%

The correlation functions of certain random antiferromagnetic spin-1∕2 critical chains

Getelina

Hoyos

2020

Eur. Phys. J. B

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We study the spin-spin correlations in two distinct random critical XX spin-1/2 chain models via exact diagonalization. For the well-known case of uncorrelated random coupling constants, we study the non-universal numerical prefactors and relate them to the corresponding Lyapunov exponent of the underlying single-parameter scaling theory. We have also obtained the functional form of the correct scaling variables important for describing even the strongest finite-size effects. Finally, with respect to the distribution of the correlations, we have numerically determined that they converge to a universal (disorder-independent) non-trivial and narrow distribution when properly rescaled by the spin-spin separation distance in units of the Lyapunov exponent. With respect to the less known case of correlated coupling constants, we have determined the corresponding exponents and shown that both typical and mean correlations functions decay algebraically with the distance. While the exponents of the transverse typical and mean correlations are nearly equal, implying a narrow distribution of transverse correlations, the longitudinal typical and mean correlations critical exponents are quite distinct implying much broader distributions. Further comparisons between this models are given.

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“…For the standard, gradient-free contact process, such a quenched disorder is known to alter the critical behavior, giving rise to singularities also in an extended region around the critical point [14]. According to a real-space renormalization method, also known as strong-disorder renormalization group (SDRG) [15], the dynamical scaling of the model in one [16] and two dimensions [17] is ultra-slow [18] and static exponents differ from those of the clean system, related to the infinite-disorder fixed point of the transformation. Whether this type of behavior is valid for any weak randomness requires further investigations.…”

Section: Introductionmentioning

confidence: 99%

Population boundary across an environmental gradient: Effects of quenched disorder

Juhász

Kovács

2020

Phys. Rev. Research

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Climatic response of population boundaries, known as ecotone, is a classic indicator in ecology. In addition to known challenges, the spatial and dynamical characteristics of the boundary are not only affected by the spatial gradient in the environmental factors, but also by local heterogeneities in the regional characteristics. Here, we capture the effects of time-independent, quenched spatial heterogeneities on the ecological boundary with the disordered contact process in one and two dimensions with a linear spatial trend in the local control parameter. We apply the strongdisorder renormalization group method to calculate the sites occupied with an O(1) probability in the stationary state, readily yielding the population front's position as the outermost site locally as well as globally for the entire boundary. We show that under a quasistatic change of the global environment, mimicking climate change, the front advances intermittently: long quiescent periods are interrupted by rare but long jumps. The characteristics of this intermittent dynamics are found to obey universal scaling laws in terms of the gradient, conjectured to be related to the correlation-length exponent of the model. In the two dimensional case our analysis shows that both the local and global shift of the front exhibit intermittent dynamics and follow the same scaling laws as in one dimension, apart from a logarithmic correction for global shifts. In one dimension, we show that determining the front position is related to an extremal problem of random walks, shedding further light on the origin of the jumps. Our results are in stark contrast to the behavior of the model without disorder, suggesting that current observations might misleadingly show little to no climate response for an extended period of time, concealing the long-term effects of climate change.

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Strong disorder RG approach – a short review of recent developments

Cited by 84 publications

References 303 publications

Strange metal state near quantum superconductor-metal transition in thin films

Strange metal state near quantum superconductor-metal transition in thin films

The correlation functions of certain random antiferromagnetic spin-1∕2 critical chains

Population boundary across an environmental gradient: Effects of quenched disorder

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