Condensed Matter

We study a network model on the Kagome lattice (NMKL). This model generalizes the Chalker-Coddington (CC) network model for the integer quantum Hall transition. Unlike random network models we studied earlier, the geometry of the Kagome lattice is regular. Therefore, we expect that the critical behavior of the NMKL should be the same as that of the CC model. We numerically compute the localization length index ν in the NKML. Our result ν=2.658±0.046 is close to CC model values obtained in a number of recent papers. We also map the NMKL to the Dirac fermions in random potentials and in a fixed periodic curvature background. The background turns out irrelevant at long scales. Our numerical and analytical results confirm our expectation of the universality of critical behavior on regular network models.

The presence of both critical behavior and oscillating patterns in brain dynamics is a very interesting issue. In this paper, we consider a model for a neuron population, where each neuron is modeled by an over-damped rotator. We find that in the space of external parameters, there exist some regions that system shows synchronization. Interestingly, just at the transition point, the avalanche statistics show a power-law behavior. Also, in the case of small systems, the (partially) synchronization and power-law behavior can happen at the same time.

We show that soft spheres interacting with a linear ramp potential when overcompressed beyond the jamming point fall in an amorphous solid phase which is critical, mechanically marginally stable and share many features with the jamming point itself. In the whole phase, the relevant local minima of the potential energy landscape display an isostatic contact network of perfectly touching spheres whose statistics is controlled by an infinite lengthscale. Excitations around such energy minima are non-linear, system spanning, and characterized by a set of non-trivial critical exponents. We perform numerical simulations to measure their values and show that, while they coincide, within numerical precision, with the critical exponents appearing at jamming, the nature of the corresponding excitations is richer. Therefore, linear soft spheres appear as a novel class of finite dimensional systems that self-organize into new, critical, marginally stable, states.

In critical systems, the effect of a localized perturbation affects points that are arbitrarily far from the perturbation location. In this paper, we study the effect of localized perturbations on the solution of the random dimer problem in 2D . By means of an accurate numerical analysis, we show that a local perturbation of the optimal covering induces an excitation whose size is extensive with finite probability. We compute the fractal dimension of the excitations and scaling exponents. In particular, excitations in random dimer problems on non-bipartite lattices have the same statistical properties of domain walls in the 2D spin glass. Excitations produced in bipartite lattices, instead, are compatible with a loop-erased self-avoiding random walk process. In both cases, we find evidence of conformal invariance of the excitations that is compatible with SLE κ with parameter κ depending on the bipartiteness of the underlying lattice only.

Numerically we study the bulk current relaxation in percolative Random Resistor cum Tunneling Network (RRTN) model through a first-passage route. The RRTN considers an extra semi-classical barrier-crossing process over a voltage threshold within a framework of classical RRN bond percolation model. We identify the different temporal regimes of relaxation and corresponding phenomenological time-scales, which fix up the extents of different regimes. These time-scales were previously identified in refs. \cite{relax-physicaA, aksubh}. We investigate on the distributions of these time-scales and observe that there exists a perfect correlation among them in the thermodynamic limit. We conclude that there exists a single time-scale which controls the RRTN dynamics. The variation of mean first-passage time .vs. system size seems to be due to sub-diffusive motion of charge carrier through the network.

The dynamics of micrometer-sized magnetic domains in ultra-thin ferromagnetic films is so dramatically slowed down by quenched disorder that the spontaneous elastic tension collapse becomes unobservable at ambient temperature. By magneto-optical imaging we show that a weak zero-bias AC magnetic field can assist such curvature-driven collapse, making the area of a bubble to reduce at a measurable rate, in spite of the negligible effect that the same curvature has on the average creep motion driven by a comparable DC field. An analytical model explains this phenomenon quantitatively.

Our work intends to show that: (1) Quantum Neural Networks (QNN) can be mapped onto spin-networks, with the consequence that the level of analysis of their operation can be carried out on the side of Topological Quantum Field Theories (TQFT); (2) Deep Neural Networks (DNN) are a subcase of QNN, in the sense that they emerge as the semiclassical limit of QNN; (3) a number of Machine Learning (ML) key-concepts can be rephrased by using the terminology of TQFT. Our framework provides as well a working hypothesis for understanding the generalization behavior of DNN, relating it to the topological features of the graphs structures involved.

Recent experiments show striking unexpected features when alternating square magnetic field pulses are applied to ferromagnetic samples: domains show area reduction and domain walls change their roughness. We explain these phenomena with a simple scalar-field model, using a numerical protocol that mimics the experimental one. For a bubble and a stripe domain, we reproduce the experimental findings: The domains shrink by a combination of linear and exponential behavior. We also reproduce the roughness exponents found in the experiments. Finally, our simulations explain the area loss by the interplay between disorder effects and effective fields induced by the local domain curvature.

The time that waves spend inside 1D random media with the possibility of performing Lévy walks is experimentally and theoretically studied. The dynamics of quantum and classical wave diffusion has been investigated in canonical disordered systems via the delay time. We show that a wide class of disorder--Lévy disorder--leads to strong random fluctuations of the delay time; nevertheless, some statistical properties such as the tail of the distribution and the average of the delay time are insensitive to Lévy walks. Our results reveal a universal character of wave propagation that goes beyond standard Brownian wave-diffusion.

For the 2D Ising model, we analyzed dependences of thermodynamic characteristics on number of spins by means of computer simulations. We compared experimental data obtained using the Fisher-Kasteleyn algorithm on a square lattice with N=l×l spins and the asymptotic Onsager solution ( N→∞ ). We derived empirical expressions for critical parameters as functions of N and generalized the Onsager solution on the case of a finite-size lattice. Our analytical expressions for the free energy and its derivatives (the internal energy, the energy dispersion and the heat capacity) describe accurately the results of computer simulations. We showed that when N increased the heat capacity in the critical point increased as lnN . We specified restrictions on the accuracy of the critical temperature due to finite size of our system. Also in the finite-dimensional case, we obtained expressions describing temperature dependences of the magnetization and the correlation length. They are in a good qualitative agreement with the results of computer simulations by means of the dynamic Metropolis Monte Carlo method.