Large q expansion of the 2D q-states Potts model

We present a recursive method to calculate a large q expansion of the 2d q-states Potts model free energies based on the Fortuin-Kasteleyn representation of the model. With this procedure, we compute directly the ordered phase partition function up to order 10 in 1/sqrt{q}. The energy cumulants at the transition can be obtained with suitable resummation and come out large for q less or around 15. As a consequence, expansions of the free energies around the transition temperature are useless for not large enough values of q. In particular the pure phase specific heats are predicted to be much larger, at q < 15, than the values extracted from current finite size scaling analysis of extrema, whereas they agree very well with recent values extracted at the transition point.Comment: 31 pages (tex) including 15 figures (Postscript

Critical Behavior of the Antiferromagnetic Heisenberg Model on a Stacked Triangular Lattice

We estimate, using a large-scale Monte Carlo simulation, the critical exponents of the antiferromagnetic Heisenberg model on a stacked triangular lattice. We obtain the following estimates: $\gamma/\nu= 2.011 \pm .014$, $\nu= .585 \pm .009$. These results contradict a perturbative $2+\epsilon$ Renormalization Group calculation that points to Wilson-Fisher O(4) behaviour. While these results may be coherent with $4-\epsilon$ results from Landau-Ginzburg analysis, they show the existence of an unexpectedly rich structure of the Renormalization Group flow as a function of the dimensionality and the number of components of the order parameter.Comment: Latex file, 10 pages, 1 PostScript figure. Was posted with a wrong Title !

Resampling technique applied to statistics of microsegregation characterization

Characterization of chemical heterogeneities at the dendrite scale is of practical importance for understanding phase transformation either during solidification or during subsequent solid-state treatment. Spot analysis with electron probe is definitely well-suited to investigate such heterogeneities at the micron scale that is relevant for most solidified products. However, very few has been done about the statistics of experimental solute distributions gained from such analyses when they are now more and more used for validating simulation data. There are two main sources generating discrepancies between estimated and actual solute distributions in an alloy: i) data sampling with a limited number of measurements to keep analysis within a reasonable time length; and ii) uncertainty linked to the measurement process, namely the physical noise that accompanies X-ray emission. Focusing on the first of these sources, a few 2-D composition images have been generated by phase field modelling of a Mg-Al alloy. These images were then used to obtain "true" solute distributions to which to compare coarse grid analyses as generally performed with a microanalyser. Resampling, i.e. generating several distributions by grid analyses with limited number of picked-up values, was then used to get statistics of estimates of solute distribution. The discussion of the present results deals first with estimating the average solute content and then focuses on the distribution in the primary phase

Critical behavior of the antiferromagnetic Heisenberg model on a stacked triangular lattice

URL: http://www-spht.cea.fr/articles/T93/015 http://fr.arxiv.org/abs/cond-mat/9302019International audienceWe estimate, using Monte Carlo simulation, the critical exponents of the anti-ferromagnetic $O(3)$ model on a stacked triangular lattice. We get $\gamma /\nu = 2.01 \pm .03,$ $\nu =.79\pm .03.$ This is compatible with the $O(4)$ fixed point, as suggested by the $2+\epsilon$ expansion, and in disagreement with the $4-\epsilon$ expansion. Our results are in contradiction with previous Monte Carlo estimates

Effect of alloying on mechanical properties of as cast ferritic nodular cast irons

The development of low temperature applications for ferritic nodular cast irons calls for improved materials in the as cast state, e.g. for off-shore windmills components. Within this line of work, a series of 68 castings were prepared with the same casting procedure and slight changes in composition. The tensile properties at room temperature, as well as the impact energy for rupture at room temperature, 220 °C and 240 °C, were measured. Outputs from multivariate analysis performed on the data are then discussed and compared to literature results, putting emphasis on the properties of the ferritic matrix

The free energy of the Potts model: from the continuous to the first-order transition region

We present a large $q$ expansion of the 2d $q$-states Potts model free energies up to order 9 in $1/\sqrt{q}$. Its analysis leads us to an ansatz which, in the first-order region, incorporates properties inferred from the known critical regime at $q=4$, and predicts, for $q>4$, the $n^{\rm th}$ energy cumulant scales as the power $(3 n /2-2)$ of the correlation length. The parameter-free energy distributions reproduce accurately, without reference to any interface effect, the numerical data obtained in a simulation for $q=10$ with lattices of linear dimensions up to L=50. The pure phase specific heats are predicted to be much larger, at $q\leq10$, than the values extracted from current finite size scaling analysis of extrema. Implications for safe numerical determinations of interface tensions are discussed.Comment: 11 pages, plain tex with 3 Postscript figures included Postscript file available by anonymous ftp://amoco.saclay.cea.fr/pubs.spht/93-022.p

Influences of ingredients and bakers on the bacteria and fungi in sourdough starters and bread

Sourdough starters are naturally occurring microbial communities in which the environment, ingredients, and bakers are potential sources of microorganisms. The relative importance of these pools remains unknown. Here, bakers from two continents used a standardized recipe and ingredients to make starters that were then baked into breads. We characterized the fungi and bacteria associated with the starters, bakers' hands, and ingredients using 16S and internal transcribed spacer (ITS) rRNA gene amplicon sequencing and then measured dough acidity and bread flavor. Starter communities were much less uniform than expected, and this variation manifested in the flavor of the bread. Starter communities were most similar to those found in flour but shared some species with the bakers' skin. While humans likely contribute microorganisms to the starters, the reverse also appears to be true. This bidirectional exchange of microorganisms between starters and bakers highlights the importance of microbial diversity on bodies and in our environments as it relates to foods. IMPORTANCE Sourdough starters are complex communities of yeast and bacteria which confer characteristic flavor and texture to sourdough bread. The microbes present in starters can be sourced from ingredients or the baking environment and are typically consistent over time. Herein, we show that even when the recipe and ingredients for starter and bread are identical, different bakers around the globe produce highly diverse starters which then alter bread acidity and flavor. Much of the starter microbial community comes from bread flour, but the diversity is also associated with differences in the microbial community on the hands of bakers. These results indicate that bakers may be a source for yeast and bacteria in their breads and/or that bakers' jobs are reflected in their skin microbiome

Dynamical Properties of a Haldane Gap Antiferromagnet

We study the dynamic spin correlation function of a spin one antiferromagnetic chain with easy-plane single-ion anisotropy. We use exact diagonalization by the Lancz\H os method for chains of lengths up to N=16 spins. We show that a single-mode approximation is an excellent description of the dynamical properties. A variational calculation allows us to clarify the nature of the excitations. The existence of a two-particle continuum near zero wavevector is clearly seen both in finite-size effects and in the dynamical structure factor. The recent neutron scattering experiments on the quasi-one-dimensional antiferromagnet NENP are fully explained by our results.Comment: 14 pages, SphT/92-135 plain tex with Postscript figures included. Postscipt file available by anonymous ftp at amoco.saclay.cea.fr by get pubs.spht/92-135.ps local_file (290 kb) or get pubs.spht/92-135.ps.Z local_file.Z (compressed - 120 kb

Active Mg Estimation Using Thermal Analysis: A Rapid Method to Control Nodularity in Ductile Cast Iron Production

Appropriate nodularity in ductile iron castings is strongly associated with the presence of high enough not combined Mg dissolved in the melt to cast. However, the residual Mg which is commonly measured for production control accounts for both dissolved Mg and Mg combined as oxides and sulfides. To account for the uncertainties associated with such a control, it is quite usual to over treat the melt with the risk of porosity appearance. A new methodology based on thermal analysis has been developed in the present work so as to estimate the amount of free Mg dissolved in the melt ready for pouring. A combination of Te mixture and a new “reactive mixture” composed of sulfur plus a commercial inoculant has been prepared for this purpose. This reactive mixture is able to transform the magnesium remaining dissolved in the melt to combined forms of this element. Experiments performed both during start of production (when Mg overtreatment is usual) and during normal mass production indicate that important variations of free Mg occur without relevant changes in residual Mg content as determined by spectrometry. The method developed in the present work has shown to be highly effective to detect those melt batches where active Mg content is not high enough for guaranteeing a correct nodularity of castings. Selection of proper active Mg thresholds and a correct inoculation process are critical to avoid “false”-negative results when using this new method