Irreducible free energy expansion and overlaps locking in mean field spin glasses

We introduce a diagrammatic formulation for a cavity field expansion around the critical temperature. This approach allows us to obtain a theory for the overlap's fluctuations and, in particular, the linear part of the Ghirlanda-Guerra relationships (GG) (often called Aizenman-Contucci polynomials (AC)) in a very simple way. We show moreover how these constraints are "superimposed" by the symmetry of the model with respect to the restriction required by thermodynamic stability. Within this framework it is possible to expand the free energy in terms of these irreducible overlaps fluctuations and in a form that simply put in evidence how the complexity of the solution is related to the complexity of the entropy.Comment: 19 page

Correlated adaptation of agents in a simple market: a statistical physics perspective

We discuss recent work in the study of a simple model for the collective behaviour of diverse speculative agents in an idealized stockmarket, considered from the perspective of the statistical physics of many-body systems. The only information about other agents available to any one is the total trade at time steps. Evidence is presented for correlated adaptation and phase transitions/crossovers in the global volatility of the system as a function of appropriate information scaling dimension. Stochastically controlled irrationally of individual agents is shown to be globally advantageous. We describe the derivation of the underlying effective stochastic differential equations which govern the dynamics, and make an interpretation of the results from the point of view of the statistical physics of disordered systems.Comment: 15 Pages. 5 figure

Stability of solutions of the Sherrington-Kirkpatrick model with respect to replications of the phase space

We use real replicas within the Thouless, Anderson and Palmer construction to investigate stability of solutions with respect to uniform scalings in the phase space of the Sherrington-Kirkpatrick model. We show that the demand of homogeneity of thermodynamic potentials leads in a natural way to a thermodynamically dependent ultrametric hierarchy of order parameters. The derived hierarchical mean-field equations appear equivalent to the discrete Parisi RSB scheme. The number of hierarchical levels in the construction is fixed by the global thermodynamic homogeneity expressed as generalized de Almeida Thouless conditions. A physical interpretation of a hierarchical structure of the order parameters is gained.Comment: REVTeX4, 22 pages, second extended version to be published in Phys. Rev.

Synthesis and application of hypercrosslinked polymers with weak cation-exchange character for the selective extraction of basic pharmaceuticals from complex environmental water samples

The synthesis of high specific surface area sorbents (HXLPP-WCX) in the form of hypercrosslinked polymer microspheres with narrow particle size distributions, average particle diameters around 6 µm, and weak cation exchange (WCX) character, is described. The WCX character arises from carboxylic acid moieties in the polymers, derived from the comonomer methacrylic acid. A novel HXLPP-WCX sorbent with an attractive set of chemical and physical properties was then used in an off-line solid-phase extraction (SPE) protocol for the selective extraction of a group of basic compounds from complex environmental samples, a priority being the clean separation of the basic compounds of interest from acidic compounds and interferences. The separation power of the new sorbent for basic pharmaceuticals was compared to two commercially available, mixed-mode sorbents, namely Oasis WCX and Strata X-CW. Under identical experimental conditions, HXLPP-WCX was found to deliver both higher capacity and better selectivity in SPE than either of the two commercially available materials. In an optimised SPE protocol, the HXLPP-WCX sorbent gave rise to quantitative and selective extractions of low µg l-1 levels of basic pharmaceuticals present in 500 ml of river water and 250 ml of effluent waste water

Hydrophilic hypercrosslinked polymeric sorbents for the solid-phase extraction of polar contaminants from water

Three new hypercrosslinked polymers with hydrophilic character arising from hydroxyl moieties in their skeletons have been prepared in microsphere format and applied to the off-line solid-phase extraction (SPE) of polar compounds from water samples. For sample volumes of 1000 ml, the recoveries of various polar pesticides, such as oxamyl, methomyl, selected phenolic compounds, as well as some pharmaceuticals, were close to 90%. The HXLPP-polar polymer with the best performance characteristics was applied to real samples. Its performance was also compared to commercially available sorbents, such as LiChrolut EN (hydrophobic, hypercrosslinked), Oasis HLB (hydrophilic, macroporous) and Isolute ENV+ (hydrophilic, hypercrosslinked); the new sorbent out-performed the commercially available sorbents. The polymer was applied successfully in off-line SPE of river water samples followed by liquid chromatography and ultraviolet detection, providing a good linear range and detection limits of 0.2 μg l-1 for the majority of the compounds, with the exception of oxamyl, methomyl, guaiacol and salicylic acid where the detection limit was 0.5 μg l-1

Exact solution of a 2d random Ising model

The model considered is a d=2 layered random Ising system on a square lattice with nearest neighbours interaction. It is assumed that all the vertical couplings are equal and take the positive value J while the horizontal couplings are quenched random variables which are equal in the same row but can take the two possible values J and J-K in different rows. The exact solution is obtained in the limit case of infinite K for any distribution of the horizontal couplings. The model which corresponds to this limit can be seen as an ordinary Ising system where the spins of some rows, chosen at random, are frozen in an antiferromagnetic order. No phase transition is found if the horizontal couplings are independent random variables while for correlated disorder one finds a low temperature phase with some glassy properties.Comment: 10 pages, Plain TeX, 3 ps figures, submitted to Europhys. Let

Decay of Correlations in a Topological Glass

In this paper we continue the study of a topological glassy system. The state space of the model is given by all triangulations of a sphere with $N$ nodes, half of which are red and half are blue. Red nodes want to have 5 neighbors while blue ones want 7. Energies of nodes with other numbers of neighbors are supposed to be positive. The dynamics is that of flipping the diagonal between two adjacent triangles, with a temperature dependent probability. We consider the system at very low temperatures. We concentrate on several new aspects of this model: Starting from a detailed description of the stationary state, we conclude that pairs of defects (nodes with the "wrong" degree) move with very high mobility along 1-dimensional paths. As they wander around, they encounter single defects, which they then move "sideways" with a geometrically defined probability. This induces a diffusive motion of the single defects. If they meet, they annihilate, lowering the energy of the system. We both estimate the decay of energy to equilibrium, as well as the correlations. In particular, we find a decay like $t^{-0.4}$

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