Employing transformations of planar Ising models (decoration-decimation followed by star-triangle), the frustrated antiferromagnetic kagome Ising model is mapped to the known disordered region of the ferromagnetic triangular Ising model. Thereafter, with supplemental aid of mapping theorems and linear algebraic correlation identities, correlations in the frustrated kagome Ising model are determined at all temperatures, enabling exact solutions to be obtained in the neutron scattering problem. More particularly, the scattering function S-xx((q) over right arrow, omega) is uniform in momentum (q) over right arrow and exhibits Dirac delta functions at select scattering frequencies, where each select frequency is associated with a temperature-dependent scattering amplitude. The scattering solutions are compared with those of the ferromagnetic kagome Ising model.

A perturbative framework is developed within the standard nonequilibrium field theory techniques to incorporate a temperature gradient across a thermoelectric device. The framework uses a temperature-dependent pseudo-Hamiltonian generated from the exact density matrix in the presence of nonuniform temperatures. We develop a perturbation theory for small temperature gradients in long wires and obtain the nonlinear thermal conductance as a function of temperature difference. The framework should be adaptable to more general cases of temperature inhomogeneities in either fermionic or bosonic systems.

We obtain the exact ground-state phase diagram of a generalized kagomé antiferromagnet with both pair and triplet interactions, J_{2} and J_{3}, respectively, in the presence of a magnetic field h appropriately tuned. We find that when the pair interaction J_{2}<0 dominates, the ground state is geometrically frustrated; on the other hand, the ground state is disordered but not frustrated when the triplet interaction J_{3} dominates, the boundaries between the two cases being at J_{3}=±J_{2}. The exact ground-state crossover lines between the two distinct types of disorder remain identifiable crossover curves at finite temperatures. In the frustrated domain, the ground state of the three-parameter model is identical to the ground state of the prototype one-parameter (J_{2}<0) model of geometrical frustration. Towards further understanding the frustration domain of the three-parameter model, a closed-form approximation (exact at zero temperature) determines solutions on a two-parameter subspace for induced magnetization and parallel magnetic susceptibility at finite fields h and temperatures T, the inverse susceptibility showing a Curie-Weiss behavior. We argue that the existence of an exact T=0 threshold magnetic field, below which the magnetization remains zero, indicates the existence of a gapped spectrum attributable to the presence of the triplet interaction J_{3}.

A model based on random matrix theory (RMT) is used to obtain the full conductance distribution $P(g)$ in three dimensions (3D) across the Anderson metal-insulator transition, and compared with the corresponding quasi-one-dimensional (Q1D) case where there is only a smooth crossover. We show that while the differences between the two are subtle, the details of the results from the RMT model agree very well with the existing numerical studies of the tight-binding Anderson model in 3D vs Q1D, including the critical region in 3D.

We present a review of the role of hierarchical relaxation processes on the dynamics of geometrically frustrated systems and specifically the low temperature dynamics of the glass states of solid ortho-para hydrogen, orientational and quadrupolar glasses, and solid N-2-Ar mixtures. Comparison is made with the dynamics observed for the recently discovered Bose glass states.

We reviewed some recent ideas to improve the efficiency and power output of thermoelectric nano-devices. We focused on two essentially independent aspects: (i) increasing the charge current by taking advantage of an interplay between the material and the thermodynamic parameters, which is only available in the non-linear regime; and (ii) decreasing the heat current by using nanowires with surface disorder, which helps excite localized phonons at random positions that can strongly scatter the propagating phonons carrying the thermal current.

We consider several limiting cases of the joint probability distribution for a random matrix ensemble with an additional interaction term controlled by an exponent γ (called the γ ensembles). The effective potential, which is essentially the single-particle confining potential for an equivalent ensemble with γ=1 (called the Muttalib-Borodin ensemble), is a crucial quantity defined in solution to the Riemann-Hilbert problem associated with the γ ensembles. It enables us to numerically compute the eigenvalue density of γ ensembles for all γ>0. We show that one important effect of the two-particle interaction parameter γ is to generate or enhance the nonmonotonicity in the effective single-particle potential. For suitable choices of the initial single-particle potentials, reducing γ can lead to a large nonmonotonicity in the effective potential, which in turn leads to significant changes in the density of eigenvalues. For a disordered conductor, this corresponds to a systematic decrease in the conductance with increasing disorder. This suggests that appropriate models of γ ensembles can be used as a possible framework to study the effects of disorder on the distribution of conductances.

We demonstrate a method to solve a general class of random matrix ensembles numerically. The method is suitable for solving log-gas models with biorthogonal type two-body interactions and arbitrary potentials. We reproduce standard results for a variety of well-known ensembles and show some new results for the Muttalib-Borodin ensembles and recently introduced $γ$-ensemble for which analytic results are not yet available.

We introduce a log-gas model that is a generalization of a random matrix ensemble with an additional interaction, whose strength depends on a parameter . The equilibrium density is computed by numerically solving the Riemann–Hilbert problem associated with the ensemble. The effect of the additional parameter associated with the two-body interaction can be understood in terms of an effective -dependent single-particle confining potential.

Experimental observation of highly reduced thermal conductivity in surface-roughness dominated silicon nanowires have generated renewed interest in low-dimensional thermoelectric devices. Using a previous work where the scattering of phonons from a rough surface is mapped to scattering from randomly situated localized phonons in the bulk of a smooth nanowire, we consider the thermal current across a nanowire for various strengths of surface disorder. We use non-equilibrium Green?s function techniques that allow us to evaluate the thermal current beyond the linear response regime, for arbitrary cold and hot temperatures of the two semi-infinite connecting leads. We show how the surface-roughness affects the frequency dependence of the thermal current, eventually leading to a temperature dependent reduction of the net current at high temperatures. We use a universal disorder parameter to describe the surface-roughness as has been proposed, and show that the dependence of the net current on this parameter provides a natural explanation for the experimentally observed differences between smooth versus rough surfaces. We argue that a systematic study of the thermal current for different values of the temperature difference between the two sides of a surface-roughness dominated nanowire for various strengths of disorder would help in our understanding of how best to optimize the thermoelectric efficiency.

The standard two-parameter (nearest-neighbor pair-interaction J2 and magnetic field h) planar Ising model ferromagnet only has phase transitions in zero field. We generalize a standard kagomé Ising model ferromagnet by adding localized triplet Ising interactions J3. Exact solutions are obtained for the phase diagrams of the three-parameter model, demonstrating finite-field phase transitions and criticality. Necessary conditions for the latter findings include the pair-interaction parameter being ferromagnetic (J2>0), the applied field parameter competing against the intrinsic triplet-interaction parameter, the ratio of the triplet- and pair-interaction parameters residing within a determined finite symmetrical interval, and the field parameter being properly tuned, viz., tracing the pertinent field vs temperature phase boundary curve. The curvilinear shape of the phase boundary facilitates the relative strength |J3|∕J2 of the triplet interaction to be experimentally accessible. Employing generalized fluid–magnet correspondence relations, it is mathematically convenient and informative to affiliate the above magnetic phase diagrams with the corresponding fluid phase diagrams of the associated generalized kagomé lattice-gas model.

Studies of possible localization of phonons in nanomaterials have gained importance in recent years in the context of thermoelectricity where phonon-localization can reduce thermal conductivity, thereby improving the efficiency of thermoelectric devices. However, despite significant efforts, phonon-localization has not yet been observed experimentally in real materials. Here we propose that surface-roughness dominated nanowires are ideal candidates to observe localization of phonons, and show numerically that the space and time evolution of the energy generated by a heat-pulse injected at a given point shows clear signatures of phonon localization. We suggest that the same configuration might allow experimental observation of localization of phonons. Our results confirm the universality in the surface-roughness dominated regime proposed earlier, which allows us to characterize the strength of disorder by a single parameter combining the width of the wire as well as the mean height of the corrugation and its correlation length.

We analyze, both theoretically and numerically, the temperature dependent thermal conductivity \k{appa} of two-dimensional nanowires with surface roughness. Although each sample is characterized by three independent parameters - the diameter (width) of the wire, the correlation length and strength of the surface corrugation - our theory predicts that there exists a universal regime where \k{appa} is a function of a single combination of all three model parameters. Numerical simulations of propagation of acoustic phonons across thin wires confirm this universality and predict a d 1/2 dependence of \k{appa} on the diameter d.

We review the results of a wide range of nuclear magnetic resonance (NMR) measurements of the local order parameters and the molecular dynamics of solid ortho-para hydrogen mixtures and solid nitrogen-argon mixtures that form novel molecular orientational glass states at low temperatures. From the NMR measurements, the distribution of the order parameters can be deduced and, in terms of simple models, used to analyze the thermodynamic measurements of the heat capacities of these systems. In addition, studies of the dielectric susceptibilities of the nitrogen-argon mixtures are reviewed in terms of replica symmetry breaking analogous to that observed for spin glass states. It is shown that this wide set of experimental results is consistent with orientation or quadrupolar glass ordering of the orientational degrees of freedom.

Discovery of new materials and improved experimental as well as numerical techniques have led to a renewed interest in geometrically frustrated spin systems. However, there are very few exact results available that can provide a benchmark for comparison. In this work, we calculate exactly the perpendicular susceptibility.. for an Ising antiferromagnet with (i) nearest-neighbor pair interaction on a kagome lattice where strong frustration prevents long-range ordering and (ii) elementary triplet interactions on a kagome lattice which has no frustration but the system remains disordered down to zero temperature. By comparing with other known exact results with and without frustration, we propose that an appropriately temperature-scaled chi(perpendicular to) can be used as a quantitative measure of the degree of frustration in Ising spin systems.

Suppressing phonon propagation in nanowires is an essential goal towards achieving efficient thermoelectric devices. Recent experiments have shown unambiguously that surface roughness is a key factor that can reduce the thermal conductivity well below the Casimir limit in thin crystalline silicon nanowires. We use insights gained from the experimental studies to construct a simple analytically tractable model of the phonon-surface roughness interaction that provides a better theoretical understanding of the effects of surface roughness on the thermal conductivity, which could potentially help in designing better thermoelectric devices.