# Scaling and Disordered Systems

Richard F. Voss, Robert B. Laibowitz, Eileen I.

## Scaling and Disordered Systems: International Workshop and Collection of - Google книги

Anomalous Diffusion on Percolating Clusters. Magnetic Properties Near Percolation. Eugene Stanley, A. Bunde, A. Coniglio, D. Hong, P. Meakin, T. Phonon-Fracton Crossover on Fractal Lattices. Geometry and Dynamics of Fractal Systems. Quantum Percolation. Yigal Meir, Amnon Aharony, A. Brooks Harris. Nonlinear Resistor Fractal Networks. Elastic Properties of Random Systems. Elasticity and Percolation. Scaling Concepts in Porous Media. The Random Field Ising Model. Cowley, R. Birgeneau, G. Shirane, H. Higgins, W. First the nuclear contribution makes the low temperature spin contribution inaccessible and second, the bulk spin gap is estimated to be 0.

With these reservations, the data collapse shown in Fig. A replot of the C [ H , T ] two-parameter data Y. Dagan and I.

## Scaling theory of quantum resistance distributions in disordered systems

Silber, personal communication indeed shows data collapse consistent with Eq. Finally, we note that the appearance of scaling and data collapse sheds light on two interrelated subsystems of the quantum magnet. The first subsystem is formed by the local moments that contribute to the heat capacity scaling. The quantum critical scaling functions which can be exhibited by this subsystem are interesting both in their own right and as a signature of a coexisting quantum paramagnet state for the second subsystem, consisting of the remaining spins.

This coexisting quantum paramagnetic phase must involve valence bonds which may be frozen, possibly with a relic of valence-bond-solid order, or resonating, as in a quantum spin liquid and associated topological order. Balents, L. Spin liquids in frustrated magnets. Nature , — Dasgupta, C. Low-temperature properties of the random Heisenberg antiferromagnetic chain. B 22 , — Fisher, D. Random antiferromagnetic quantum spin chains. B 50 , — Bhatt, R. A scaling method for low temperature behavior of random antiferromagnetic systems invited. Paalanen, M. Thermodynamic behavior near a metal-insulator transition.

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Kimchi, I. Valence bonds in random quantum magnets: theory and application to YbMgGaO 4. X 8 , Kitagawa, K. A spin-orbital-entangled quantum liquid on a honeycomb lattice. Nature , Rau, J. Spin-orbit physics giving rise to novel phases in correlated systems: iridates and related materials. Matter Phys.

Hermanns, M. Physics of the kitaev model: fractionalization, dynamic correlations, and material connections. Sheckelton, J. Possible valence-bond condensation in the frustrated cluster magnet LiZn 2 Mo 3 O 8.

Local magnetism and spin correlations in the geometrically frustrated cluster magnet LiZn 2 Mo 3 O 8. B 89 , Mourigal, M. Molecular quantum magnetism in LiZn 2 Mo 3 O 8. Flint, R. Emergent honeycomb lattice in LiZn 2 Mo 3 O 8.

Chen, G. Cluster mott insulators and two curie-weiss regimes on an anisotropic kagome lattice.

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B 93 , Emergent orbitals in the cluster mott insulator on a breathing kagome lattice. B 97 , Helton, J. Han, T. This is in accord with our intuition in that we expect a stronger decay in a dielectric than in a conductive system. A few examples will be shown later. As an introduction to the study of CRFs derived from distributions, let us suppose that the generating DRF has two frequencies, w 1 and w 2 , with probabilities a and 1- a.

That is, Y t is given by. It is interesting to interpret this result. Figure 3. A HTDF with an asymptotic hyperbolic behavior is a common ingredient for obtaining such responses. Let us denote it, as usual, as Y t. Let us compare the two asymptotic behaviors, Eqs. The exponents add to -2, a kind of universality similar to the one obtained by SM [10] for current traces in certain disordered materials excited by a light pulse.

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In the previous sub-section we have treated the highly dispersive CRF. The two barrier system of sub-section IV. Stretched-exponentials also give rise to normal dispersive responses.

Whenever possible we have used tables [43,44] for handling inverse LTs. We took this to mean that a sufficiently good approximation was achieved. In he calculations the 5 th version of the Maple TM software facilities was used. In the following a few examples of the use of this truncated Widder method are given. In Fig. We see that the convergence becomes slower near the maximum and therefore it seems that the method is better suited to functions whose primitives are decaying functions of the time, such as DRF and CRF. Hyperbolic decay makes convergence easier.

See also Fig. Figure 4. Figure 5.

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## Scaling Phenomena in Disordered Systems

The last one may be considered visually exact. Figure 6. Approximated primitives of , using Eq. Most of the DRFs originated from ac measurements and were inferred from attempts to fit results plotted in a Cole-Cole diagram [3,19,46], involving the real and the imaginary part of the complex susceptibility. By means of either Eq. For instance, the Cole-Cole complex susceptibility derives from. Therefore, the task of finding the CRF through Eq. Some care is necessary when analyzing in the time domain a derived CRF.