On exact mappings between fermionic Ising spin glass and classical spin glass models

We present in this paper exact analytical expressions for the thermodynamical properties and Green functions of a certain family of fermionic Ising spin-glass models with Hubbard interaction, by noticing that their Hamiltonian is a function of the number operator only. The thermodynamical properties are mapped to the classical Ghatak-Sherrington spin-glass model while the the Density of States (DoS) is related to its joint spin-field distribution. We discuss the presence of the pseudogap in the DoS with the help of this mapping.Comment: 6 page

Greener and sustainable method for alkene epoxidations by polymer-supported Mo(VI) catalysts

A polybenzimidazole supported Mo(VI) (PBI.Mo) catalyst has been prepared and characterised. The catalytic activities of the PBI.Mo catalyst in epoxidation of alkenes with tert-butyl hydroperoxide (TBHP) as an oxidant have been studied under different reaction conditions in a batch reactor. As alkene representatives we have chosen cyclohexene, limonene, α-pinene and 1-octene (a less reactive terminal alkene). The order of reactivity of the alkenes was found to be: cyclohexene>limonene>α-pinene>1-octene. The stability of each polymer catalyst was assessed by recycling a sample in batch reaction using conditions that will form the basis of the continuous process. The loss of Mo from each support has been investigated by isolating any residue from the reaction supernatant solutions, following removal of the heterogeneous polymer catalyst, and then using the residues as potential catalysts in epoxidation reactions

Facile synthesis of branched pol(vinyl alcohol)s

Poly(vinyl alcohol) (PVOH) is a ubiquitous synthetic polymer that finds widespread application in biological and medical products through to personal, domestic, and industrial products. The currently available range of materials all have linear backbone architectures with interesting solubility, rheological, and interfacial properties. The latter might be significantly broadened if complementary polymers with branched backbone architectures could be synthesized, especially if the methodology involved only minor changes from that currently practiced. We have now synthesized branched PVOHs via conventional free radical copolymerization of vinyl acetate (VAc) and triallyl-triazine-trione (TTT), in 2-isopropoxy ethanol (IPE) solvent in the presence of appropriate thiol free radical chain transfer agents, followed by alcoholysis of the so-formed branched poly(vinyl acetates)s (PVAc)s with methanol. Balancing the mole ratio of TTT to thiol allows high conversion to branched materials to be achieved while inhibiting cross-linking and gelation of the products. The branch points derived from the TTT comonomer have been shown to be conserved during the alcoholysis step, and extensive characterization of the PVAc precursors and the derived PVOHs using multiple detector size exclusion chromatographic (SEC) instrumentation has confirmed the highly branched nature of both groups of polymers. Final confirmation of the branched architecture of the PVOH samples has been made by reacetylation of some samples, in effect to regenerate their PVAc precursors. SEC analysis of the latter has indeed shown these to be architecturally very similar to the original precursor PVAcs. This novel methodology for synthesizing branched PVOHs involves relatively minor adjustments to the currently used industrial process for linear PVOHs and so offers good prospects for scale-up and exploitation

Magnon Localization in Mattis Glass

We study the spectral and transport properties of magnons in a model of a disordered magnet called Mattis glass, at vanishing average magnetization. We find that in two dimensional space, the magnons are localized with the localization length which diverges as a power of frequency at small frequencies. In three dimensional space, the long wavelength magnons are delocalized. In the delocalized regime in 3d (and also in 2d in a box whose size is smaller than the relevant localization length scale) the magnons move diffusively. The diffusion constant diverges at small frequencies. However, the divergence is slow enough so that the thermal conductivity of a Mattis glass is finite, and we evaluate it in this paper. This situation can be contrasted with that of phonons in structural glasses whose contribution to thermal conductivity is known to diverge (when inelastic scattering is neglected).Comment: 11 page

Following microscopic motion in a two dimensional glass-forming binary fluid

The dynamics of a binary mixture of large and small discs are studied at temperatures approaching the glass transition using an analysis based on the topology of the Voronoi polygon surrounding each atom. At higher temperatures we find that dynamics is dominated by fluid-like motion that involves particles entering and exiting the nearest-neighbour shells of nearby particles. As the temperature is lowered, the rate of topological moves decreases and motion becomes localised to regions of mixed pentagons and heptagons. In addition we find that in the low temperature state particles may translate significant distances without undergoing changes in their nearest neig hbour shell. These results have implications for dynamical heterogeneities in glass forming liquids.Comment: 12 pages, 7 figure

Glassy behaviour in an exactly solved spin system with a ferromagnetic transition

We show that applying simple dynamical rules to Baxter's eight-vertex model leads to a system which resembles a glass-forming liquid. There are analogies with liquid, supercooled liquid, glassy and crystalline states. The disordered phases exhibit strong dynamical heterogeneity at low temperatures, which may be described in terms of an emergent mobility field. Their dynamics are well-described by a simple model with trivial thermodynamics, but an emergent kinetic constraint. We show that the (second order) thermodynamic transition to the ordered phase may be interpreted in terms of confinement of the excitations in the mobility field. We also describe the aging of disordered states towards the ordered phase, in terms of simple rate equations.Comment: 11 page

Exact Solution of the Infinite-Range Quantum Mattis Model

We have solved the quantum version of the Mattis model with infinite-range interactions. A variational approach gives the exact solution for the infinite-range system, in spite of the non-commutative nature of the quantum spin components; this implies that quantum effects are not predominant in determining the macroscopic properties of the system. Nevertheless, the model has a surprisingly rich phase behaviour, exhibiting phase diagrams with tricritical, three-phase and critical end points.Comment: 14 pages, 11 figure

Phase Diagram and Storage Capacity of Sequence Processing Neural Networks

We solve the dynamics of Hopfield-type neural networks which store sequences of patterns, close to saturation. The asymmetry of the interaction matrix in such models leads to violation of detailed balance, ruling out an equilibrium statistical mechanical analysis. Using generating functional methods we derive exact closed equations for dynamical order parameters, viz. the sequence overlap and correlation- and response functions, in the thermodynamic limit. We calculate the time translation invariant solutions of these equations, describing stationary limit-cycles, which leads to a phase diagram. The effective retarded self-interaction usually appearing in symmetric models is here found to vanish, which causes a significantly enlarged storage capacity of $\alpha_c\sim 0.269$, compared to \alpha_\c\sim 0.139 for Hopfield networks storing static patterns. Our results are tested against extensive computer simulations and excellent agreement is found.Comment: 17 pages Latex2e, 2 postscript figure

Dynamical solutions of a quantum Heisenberg spin glass model

We consider quantum-dynamical phenomena in the $\mathrm{SU}(2)$, $S=1/2$ infinite-range quantum Heisenberg spin glass. For a fermionic generalization of the model we formulate generic dynamical self-consistency equations. Using the Popov-Fedotov trick to eliminate contributions of the non-magnetic fermionic states we study in particular the isotropic model variant on the spin space. Two complementary approximation schemes are applied: one restricts the quantum spin dynamics to a manageable number of Matsubara frequencies while the other employs an expansion in terms of the dynamical local spin susceptibility. We accurately determine the critical temperature $T_c$ of the spin glass to paramagnet transition. We find that the dynamical correlations cause an increase of $T_c$ by 2% compared to the result obtained in the spin-static approximation. The specific heat $C(T)$ exhibits a pronounced cusp at $T_c$. Contradictory to other reports we do not observe a maximum in the $C(T)$-curve above $T_c$.Comment: 8 pages, 7 figure