We investigate the effects of layered quenched disorder on the behavior of planar magnets, superfluids, and superconductors by performing large-scale Monte-Carlo simulations of a three-dimensional randomly layered XY model. Our data provide numerical evidence for the recently predicted anomalously elastic (sliding) intermediate phase between the conventional high-temperature and low-temperature phases. In this intermediate phase, the spin-wave stiffness perpendicular to the layers vanishes in the thermodynamic limit while the stiffness parallel to the layers as well as the spontaneous magnetization are nonzero. In addition, the susceptibility displays unconventional finite-size scaling properties. We compare our Monte-Carlo results with the theoretical predictions, and we discuss possible experiments in ultracold atomic gases, layered superconductors and in nanostructures.
We show that a smectic in a disordered medium (e.g., aerogel) exhibits anomalous elasticity, with the compression modulus B(k) vanishing and the bend modulus K(k) diverging as k --> 0. In addition, the effective disorder develops long ranged correlations. These divergences are much stronger than those driven by thermal fluctuations in pure smectics, and are controlled by a zero temperature glassy fixed point, which we study in an $ε=5-d$ expansion. We discuss the experimental implications of these theoretical predictions.
The propagation of light through a disordered layered system is studied. It is shown that distribution function of the transmission coefficient phase tends to stationary non-uniform distribution as the number of layers increases. The exponential convergence to the stationary distribution allows unambiguous definition of the phase randomization length scale.
Disordered biopolymer gels have striking mechanical properties including strong nonlinearities. In the case of athermal gels (such as collagen-I) the nonlinearity has long been associated with a crossover from a bending dominated to a stretching dominated regime of elasticity. The physics of this crossover is related to the existence of a central-force isostatic point and to the fact that for most gels the bending modulus is small. This crossover induces scaling behavior for the elastic moduli. In particular, for linear elasticity such a scaling law has been demonstrated [Broedersz et al. Natu…
Phase transitions of a flux lattice in layered superconductors with magnetic field perpendicular to the layers and in presence of disorder are studied. We find that disorder generates a random Josephson coupling between layers which leads to a Josephson glass (JG) phase at low temperatures; vanishing of the JG order identifies a depinning transition. We also find that disorder and thermal fluctuations lead to layer decoupling where the renormalized Josephson coupling vanishes. Near decoupling an anharmonic regime is found, where usual elasticity and the resulting Bragg glass are not valid. The…
Localization of electronic states in disordered thin layered systems with b layers is studied within the Anderson model of localization using the transfer-matrix method and finite-size scaling of the inverse of the smallest Lyapunov exponent. The results support the one-parameter scaling hypothesis for disorder strengths W studied and b=1,...,6. The obtained results for the localization length are in good agreement with both the analytical results of the self-consistent theory of localization and the numerical scaling studies of the two-dimensional Anderson model. The localization length near …
The elasticity of disordered and polydisperse polymer networks is a fundamental problem of soft matter physics that is still open. Here, we self-assemble polymer networks via simulations of a mixture of bivalent and tri- or tetravalent patchy particles, which result in an exponential strand length distribution analogous to that of experimental randomly crosslinked systems. After assembly, the network connectivity and topology are frozen and the resulting system is characterized. We find that the fractal structure of the network depends on the number density at which the assembly has been carri…
We investigate the high-frequency behavior of the density of vibrational states in three-dimensional elasticity theory with spatially fluctuating elastic moduli. At frequencies well above the mobility edge, instanton solutions yield an exponentially decaying density of states. The instanton solutions describe excitations, which become localized due to the disorder-induced fluctuations, which lower the sound velocity in a finite region compared to its average value. The exponentially decaying density of states (known in electronic systems as the Lifshitz tail) is governed by the statistics of a…
Due to their unique structural and mechanical properties, randomly-crosslinked polymer networks play an important role in many different fields, ranging from cellular biology to industrial processes. In order to elucidate how these properties are controlled by the physical details of the network (\textit{e.g.} chain-length and end-to-end distributions), we generate disordered phantom networks with different crosslinker concentrations $C$ and initial density $ρ_{\rm init}$ and evaluate their elastic properties. We find that the shear modulus computed at the same strand concentration for network…
Paradigmatic model systems, which are used to study the mechanical response of matter, are random networks of point-atoms, random sphere packings, or simple crystal lattices, all of these models assume central-force interactions between particles/atoms. Each of these models differs in the spatial arrangement and the correlations among particles. In turn, this is reflected in the widely different behaviours of the shear (G) and compression (K) elastic moduli. The relation between the macroscopic elasticity as encoded in G, K and their ratio, and the microscopic lattice structure/order, is not u…
Phase fluctuations in finite thickness layered superconducting films are studied theoretically. The model consists of a set of layers, coupled to each other via a gradient-like term in the phase-only action. It is shown that the effective phase stiffness of the whole system is proportional to its thickness (i.e. the number of individual layers). This result leads to a superconductor-insulator transition and an inverse dependence of $T_c$ on thickness,$T_c\sim d^{-1}$, both in accord with the experimental findings. The relevance to disordered thin films is discussed.
Lattice Monte-Carlo simulations were performed to study the equilibrium ordering in a two-dimensional nematic system with quenched random disorder. When the disordering field, which competes against the aligning effect of the Frank elasticity, is sufficiently strong, the long-range correlation of the director orientation is found to decay as a simple exponential, Exp[-r/x]. The correlation length {x} itself also decays exponentially with increasing strength of the disordering field. This result represents a new type of behavior, distinct from the Gaussian and power-law decays predicted by some…
We show that the common local Monte Carlo rules used to simulate the motion of driven flux lines in disordered media cannot capture the interplay between elasticity and disorder which lies at the heart of these systems. We therefore discuss a class of generalized Monte Carlo algorithms where an arbitrary number of line elements may move at the same time. We prove that all these dynamical rules have the same value of the critical force and possess phase spaces made up of a single ergodic component. A variant Monte Carlo algorithm allows to compute the critical force of a sample in a single pass…
We study the ferromagnetic phase transition in a randomly layered Heisenberg magnet using large-scale Monte-Carlo simulations. Our results provide numerical evidence for the infinite-randomness scenario recently predicted within a {strong-disorder renormalization group approach}. Specifically, we investigate the finite-size scaling behavior of the magnetic susceptibility which is characterized by a non-universal power-law divergence in the Griffiths phase. We also study the perpendicular and parallel spin-wave stiffnesses in the Griffiths phase. In agreement with the theoretical predictions, t…
The low-temperature thermal and transport properties of an unusual kind of crystal exhibiting minimal molecular positional and tilting disorder have been measured. The material, namely, low-dimensional, highly anisotropic pentachloronitrobenzene (PCNB) has a layered structure of rhombohedral parallel planes in which the molecules execute large-amplitude in-plane as well as concurrent out-of-plane librational motions. Our study reveals that low-temperature glassy anomalies can be found in a system with minimal disorder due to the freezing of (mostly in-plane) reorientational jumps of molecules …
The transport characteristics of a disordered MoS$_2$ nanoflake in the insulator regime are studied by electrical and magnetotransport measurements. The layered MoS$_2$ nanoflake is exfoliated from a bulk MoS$_2$ crystal and the conductance $G$ and magnetoresistance are measured in a four-probe setup over a wide range of temperatures. At high temperatures, we observe that $\log_{10}G$ exhibits a $-T^{-1}$ temperature dependence and the transport in the nanoflake dominantly arises from thermal activation. At low temperatures, where the transport in the nanoflake dominantly takes place via varia…
