Bose glass behavior in (Yb1−x_{1-x}Lux_x)4_4As3_3 representing the randomly diluted quantum spin-1/2 chains

The site-diluted compound (Yb$_{1-x}$Lu$_x$)$_4$As$_3$ is a scarce realization of the linear Heisenberg antiferromagnet partitioned into finite-size segments and is an ideal model compound for studying field-dependent effects of quenched disorder in the one-dimensional antiferromagnets. It differentiates from the systems studied so far in two aspects - the type of randomness and the nature of the energy gap in the pure sample. We have measured the specific heat of single-crystal (Yb$_{1-x}$Lu$_x$)$_4$As$_3$ in magnetic fields up to 19.5 T. The contribution $C_{\perp}$ arising from the magnetic subsystem in an applied magnetic field perpendicular to the chains is determined. Compared to pure Yb$_4$As$_3$, for which $C_{\perp}$ indicates a gap opening, for diluted systems a non-exponential decay is found at low temperatures which is consistent with the thermodynamic scaling of the specific heat established for a Bose-glass phase.Comment: 8 pages, 17 figures, including supplemental material, accepted for PRB rapid communicatio

The critical Ising lines of the d=2 Ashkin-Teller model

The universal critical point ratio $Q$ is exploited to determine positions of the critical Ising transition lines on the phase diagram of the Ashkin-Teller (AT) model on the square lattice. A leading-order expansion of the ratio $Q$ in the presence of a non-vanishing thermal field is found from finite-size scaling and the corresponding expression is fitted to the accurate perturbative transfer-matrix data calculations for the $L\times L$ square clusters with $L\leq 9$.Comment: RevTex, 4 pages, two figure

Cumulant ratios and their scaling functions for Ising systems in strip geometries

We calculate the fourth-order cumulant ratio (proposed by Binder) for the two-dimensional Ising model in a strip geometry L x oo. The Density Matrix Renormalization Group method enables us to consider typical open boundary conditions up to L=200. Universal scaling functions of the cumulant ratio are determined for strips with parallel as well as opposing surface fields.Comment: 4 pages, RevTex, one .eps figure; references added, format change

Combinatorics of bicubic maps with hard particles

We present a purely combinatorial solution of the problem of enumerating planar bicubic maps with hard particles. This is done by use of a bijection with a particular class of blossom trees with particles, obtained by an appropriate cutting of the maps. Although these trees have no simple local characterization, we prove that their enumeration may be performed upon introducing a larger class of "admissible" trees with possibly doubly-occupied edges and summing them with appropriate signed weights. The proof relies on an extension of the cutting procedure allowing for the presence on the maps of special non-sectile edges. The admissible trees are characterized by simple local rules, allowing eventually for an exact enumeration of planar bicubic maps with hard particles. We also discuss generalizations for maps with particles subject to more general exclusion rules and show how to re-derive the enumeration of quartic maps with Ising spins in the present framework of admissible trees. We finally comment on a possible interpretation in terms of branching processes.Comment: 41 pages, 19 figures, tex, lanlmac, hyperbasics, epsf. Introduction and discussion/conclusion extended, minor corrections, references adde

Response of a catalytic reaction to periodic variation of the CO pressure: Increased CO_2 production and dynamic phase transition

We present a kinetic Monte Carlo study of the dynamical response of a Ziff-Gulari-Barshad model for CO oxidation with CO desorption to periodic variation of the CO presure. We use a square-wave periodic pressure variation with parameters that can be tuned to enhance the catalytic activity. We produce evidence that, below a critical value of the desorption rate, the driven system undergoes a dynamic phase transition between a CO_2 productive phase and a nonproductive one at a critical value of the period of the pressure oscillation. At the dynamic phase transition the period-averged CO_2 production rate is significantly increased and can be used as a dynamic order parameter. We perform a finite-size scaling analysis that indicates the existence of power-law singularities for the order parameter and its fluctuations, yielding estimated critical exponent ratios $\beta/\nu \approx 0.12$ and $\gamma/\nu \approx 1.77$. These exponent ratios, together with theoretical symmetry arguments and numerical data for the fourth-order cumulant associated with the transition, give reasonable support for the hypothesis that the observed nonequilibrium dynamic phase transition is in the same universality class as the two-dimensional equilibrium Ising model.Comment: 18 pages, 10 figures, accepted in Physical Review

Two dimensional Ising spin glasses with non-zero ordering temperatures

We demonstrate numerically that for Ising spins on square lattices with ferromagnetic second neighbour interactions and random near neighbour interactions, two dimensional Ising spin glass order with a non-zero freezing temperature can occur. We compare some of the physical properties of these spin glasses with those of standard spin glasses in higher dimensions.Comment: 9 page latex file and 9 ps figures. To appear in Phys. Rev. Let

Critical behavior of hard-core lattice gases: Wang-Landau sampling with adaptive windows

Critical properties of lattice gases with nearest-neighbor exclusion are investigated via the adaptive-window Wang-Landau algorithm on the square and simple cubic lattices, for which the model is known to exhibit an Ising-like phase transition. We study the particle density, order parameter, compressibility, Binder cumulant and susceptibility. Our results show that it is possible to estimate critical exponents using Wang-Landau sampling with adaptive windows. Finite-size-scaling analysis leads to results in fair agreement with exact values (in two dimensions) and numerical estimates (in three dimensions).Comment: 20 pages, 11 figure

Series expansions from the corner transfer matrix renormalization group method: the hard squares model

The corner transfer matrix renormalization group method is an efficient method for evaluating physical quantities in statistical mechanical models. It originates from Baxter's corner transfer matrix equations and method, and was developed by Nishino and Okunishi in 1996. In this paper, we review and adapt this method, previously used for numerical calculations, to derive series expansions. We use this to calculate 92 terms of the partition function of the hard squares model. We also examine the claim that the method is subexponential in the number of generated terms and briefly analyse the resulting series.Comment: 10 figure

the role of soluble and insoluble fibers during fermentation of Chicory root pulp

This thesis was aimed at understanding the in vitro fermentability of soluble and insoluble fibers in chicory root pulp (CRP). First, CRP and ensiled chicory root pulp (ECRP) were characterized for cell wall polysaccharides (CWPs). Both CRP and ECRP were rich in CWPs (56-58 w/w (%)) and had rather similar sugar compositions. The CWPs consist of 62 % pectin, 11% hemicellulose and 27% cellulose. Pectin and xyloglucan were acetylated and the rhamnogalacturonan-I segments of pectin were branched mostly with arabinan. Compared to CRP, ECRP has four times more soluble pectin. In vitrofermentability in a batch model for 24 h using human faecal inoculum, showed that fibers in both CRP (51% carbohydrate utilisation) and ECRP (59% carbohydrate utilisation) were fermentable, especially pectin (80-87%). The increased levels of soluble pectin (arabinan, homogalacturonan and galactan) and the hypothesized open cell wall structure in ECRP contributed to a quicker fermentation and a higher level of carbohydrate utilization compared to CRP. In contrast to batch fermentation, fermentation in the dynamic TNO In vitro model of the colon (TIM-2) was rapid (57% carbohydrate utilisation in 2 h). ECRP carbohydrates (85%) were less fermented in 24 h compared to CRP carbohydrates (92%) due to lower utilisation of ECRP insoluble fibers than CRP insoluble fibers. It was hypothesized that soluble fibers that are readily fermentable and dominantly present in ECRP, programmed the microbiota in TIM-2 to fully adapt to these soluble fibers. After their utilization, the microbiota was not able to adapt towards the fermentation of insoluble fibers. Analysis of enzyme activities during batch fermentation of CRP showed increased levels of arabinofuranosidase, β-galactosidase, endo-arabinanase, endo-galactanase, exo-polygalacturonase, pectin de-esterifying enzymes and endo-polygalacturonase. They synergistically contributed to degrading pectin in CRP from 12 to 24 h of fermentation.</p