Thermodynamics of the S=1 spin ladder as a composite S=2 chain model

A special class of S=1 spin ladder hamiltonians, with second- neighbor exchange interactions and with anisotropies in the $z$-direction, can be mapped onto one-dimensional composite S=2 (tetrahedral S=1) models. We calculate the high temperature expansion of the Helmoltz free energy for the latter class of models, and show that their magnetization behaves closely to that of standard XXZ models with a suitable effective spin $S_{eff}$, such that $S_{eff}(1+S_{eff})=$, where ${\bf S}_i$ refers to the components of spin in the composite model. It is also shown that the specific heat per site of the composite model, on the other hand, can be very different from that of the effective spin model, depending on the parameters of the hamiltonian.Comment: 17 pages, 4 figures. Submitted for publicatio

Distribution of forensic marker allelic frequencies in pernambuco, Northestern Brazil

7siPernambuco is one of the 27 federal units of Brazil, ranking seventh in the number of inhabitants. We examined the allele frequencies of 13 short tandem repeat loci (CFS1PO, D3S1358, D5S818, D7S820, D8S1179, D13S317, D16S539, D18S51, D21S11, FGA, TH01, vWA, and TPOX), the minimum recommended by the Federal Bureau of Investigation and commonly used in forensic genetics laboratories in Brazil, in a sample of 609 unrelated individuals from all geographic regions of Pernambuco. The allele frequencies ranged from 5 to 47.2%. No significant differences for any loci analyzed were observed compared with other publications in other various regions of Brazil. Most of the markers observed were in Hardy-Weinberg equilibrium. The occurrence of the allele 47.2 (locus FGA) and alleles 35.1 and 39 (locus D21S11), also described in a single study of the Brazilian population, was observed. The other forensic parameters analyzed (matching probability, power of discrimination, polymorphic information content, paternity exclusion, complement factor I, observed heterozygosity, expected heterozygosity) indicated that the studied markers are very informative for human forensic identification purposes in the Pernambuco population.openopenSantos, S.M.; Souza, C.A.; Rabelo, K.C.N.; Souza, P.; Moura, R.R.; Oliveira, T.C.; Crovella, S.Santos, S. M.; Souza, C. A.; Rabelo, K. C. N.; Souza, P.; Moura, R. R.; Oliveira, T. C.; Crovella, Sergi

A set of exactly solvable Ising models with half-odd-integer spin

We present a set of exactly solvable Ising models, with half-odd-integer spin-S on a square-type lattice including a quartic interaction term in the Hamiltonian. The particular properties of the mixed lattice, associated with mixed half-odd-integer spin-(S,1/2) and only nearest-neighbour interaction, allow us to map this system either onto a purely spin-1/2 lattice or onto a purely spin-S lattice. By imposing the condition that the mixed half-odd-integer spin-(S,1/2) lattice must have an exact solution, we found a set of exact solutions that satisfy the {\it free fermion} condition of the eight vertex model. The number of solutions for a general half-odd-integer spin-S is given by $S+1/2$. Therefore we conclude that this transformation is equivalent to a simple spin transformation which is independent of the coordination number

Yet on statistical properties of traded volume: correlation and mutual information at different value magnitudes

In this article we analyse linear correlation and non-linear dependence of traded volume, $v$, of the 30 constituents of Dow Jones Industrial Average at different value scales. Specifically, we have raised $v$ to some real value $\alpha$ or $\beta$, which introduces a bias for small ($\alpha, \beta <0$) or large ($\alpha, \beta >1$) values. Our results show that small values of $v$ are regularly \emph{anti-correlated} with values at other scales of traded volume. This is consistent with the high liquidity of the 30 equities analysed and the asymmetric form of the multi-fractal spectrum for traded volume which has supported the dynamical scenario presented by us.Comment: 6 pages, 2 figure

The high temperature expansion of the classical XYZXYZ chain

We present the $\beta$-expansion of the Helmholtz free energy of the classical $XYZ$ model, with a single-ion anisotropy term and in the presence of an external magnetic field, up to order $\beta^{12}$. We compare our results to the numerical solution of Joyce's [Phys. Rev. Lett. 19, 581 (1967)] expression for the thermodynamics of the $XXZ$ classical model, with neither single-ion anisotropy term nor external magnetic field. This comparison shows that the derived analytical expansion is valid for intermediate temperatures such as $kT/J_x \approx 0.5$. We show that the specific heat and magnetic susceptibility of the spin-2 antiferromagnetic chain can be approximated by their respective classical results, up to $kT/J \approx 0.8$, within an error of 2.5%. In the absence of an external magnetic field, the ferromagnetic and antiferromagnetic chains have the same classical Helmholtz free energy. We show how this two types of media react to the presence of an external magnetic field

Generalized Transformation for Decorated Spin Models

The paper discusses the transformation of decorated Ising models into an effective \textit{undecorated} spin models, using the most general Hamiltonian for interacting Ising models including a long range and high order interactions. The inverse of a Vandermonde matrix with equidistant nodes $[-s,s]$ is used to obtain an analytical expression of the transformation. This kind of transformation is very useful to obtain the partition function of decorated systems. The method presented by Fisher is also extended, in order to obtain the correlation functions of the decorated Ising models transforming into an effective undecorated Ising models. We apply this transformation to a particular mixed spin-(1/2,1) and (1/2,2) square lattice with only nearest site interaction. This model could be transformed into an effective uniform spin-$S$ square lattice with nearest and next-nearest interaction, furthermore the effective Hamiltonian also include combinations of three-body and four-body interactions, particularly we considered spin 1 and 2.Comment: 16 pages, 4 figure

Consistency analysis of a nonbirefringent Lorentz-violating planar model

In this work analyze the physical consistency of a nonbirefringent Lorentz-violating planar model via the analysis of the pole structure of its Feynman propagators. The nonbirefringent planar model, obtained from the dimensional reduction of the CPT-even gauge sector of the standard model extension, is composed of a gauge and a scalar fields, being affected by Lorentz-violating (LIV) coefficients encoded in the symmetric tensor $\kappa_{\mu\nu}$. The propagator of the gauge field is explicitly evaluated and expressed in terms of linear independent symmetric tensors, presenting only one physical mode. The same holds for the scalar propagator. A consistency analysis is performed based on the poles of the propagators. The isotropic parity-even sector is stable, causal and unitary mode for $0\leq\kappa_{00}<1$. On the other hand, the anisotropic sector is stable and unitary but in general noncausal. Finally, it is shown that this planar model interacting with a $\lambda|\varphi|^{4}-$Higgs field supports compactlike vortex configurations.Comment: 11 pages, revtex style, final revised versio

Some exact solutions of F(R) gravity with charged (a)dS black hole interpretation

In this paper we obtain topological static solutions of some kind of pure $F(R)$ gravity. The present solutions are two kind: first type is uncharged solution which corresponds with the topological (a)dS Schwarzschild solution and second type has electric charge and is equivalent to the Einstein-$\Lambda$-conformally invariant Maxwell solution. In other word, starting from pure gravity leads to (charged) Einstein-$\Lambda$ solutions which we interpreted them as (charged) (a)dS black hole solutions of pure $F(R)$ gravity. Calculating the Ricci and Kreschmann scalars show that there is a curvature singularity at $r=0$. We should note that the Kreschmann scalar of charged solutions goes to infinity as $r \rightarrow 0$, but with a rate slower than that of uncharged solutions.Comment: 21 pages, 4 figures, generalization to higher dimensions, references adde

Viability of Noether symmetry of F(R) theory of gravity

Canonization of F(R) theory of gravity to explore Noether symmetry is performed treating R - 6(\frac{\ddot a}{a} + \frac{\dot a^2}{a^2} + \frac{k}{a^2}) = 0 as a constraint of the theory in Robertson-Walker space-time, which implies that R is taken as an auxiliary variable. Although it yields correct field equations, Noether symmetry does not allow linear term in the action, and as such does not produce a viable cosmological model. Here, we show that this technique of exploring Noether symmetry does not allow even a non-linear form of F(R), if the configuration space is enlarged by including a scalar field in addition, or taking anisotropic models into account. Surprisingly enough, it does not reproduce the symmetry that already exists in the literature (A. K. Sanyal, B. Modak, C. Rubano and E. Piedipalumbo, Gen.Relativ.Grav.37, 407 (2005), arXiv:astro-ph/0310610) for scalar tensor theory of gravity in the presence of R^2 term. Thus, R can not be treated as an auxiliary variable and hence Noether symmetry of arbitrary form of F(R) theory of gravity remains obscure. However, there exists in general, a conserved current for F(R) theory of gravity in the presence of a non-minimally coupled scalar-tensor theory (A. K. Sanyal, Phys.Lett.B624, 81 (2005), arXiv:hep-th/0504021 and Mod.Phys.Lett.A25, 2667 (2010), arXiv:0910.2385 [astro-ph.CO]). Here, we briefly expatiate the non-Noether conserved current and cite an example to reveal its importance in finding cosmological solution for such an action, taking F(R) \propto R^{3/2}.Comment: 16 pages, 1 figure. appears in Int J Theoretical Phys (2012

Site specific nutrient management software for coffee

Chemical fertilizers are integral part of agriculture and continue to be inevitable source of nutrients. A site specific soil test based nutrient management system ensures the judicious use of fertilizers by contributing to the sustainable and economic production without polluting the soil resources. Coffee is a major commercial crop of India and the site specific fertilizer recommendations for this crop have proved to have advantages over ‘blanket fertilization’ by improving the fertilizer use efficiency and profitability. The software was designed in such a way that entries corresponding to the block-wise soil test data viz., soil pH, available N, P and K generate necessary information on the quantity of suitable and available fertilizers that need to be applied to each block to meet the demand of the crop and plant