Transfer-Matrix Monte Carlo Estimates of Critical Points in the Simple Cubic Ising, Planar and Heisenberg Models

The principle and the efficiency of the Monte Carlo transfer-matrix algorithm are discussed. Enhancements of this algorithm are illustrated by applications to several phase transitions in lattice spin models. We demonstrate how the statistical noise can be reduced considerably by a similarity transformation of the transfer matrix using a variational estimate of its leading eigenvector, in analogy with a common practice in various quantum Monte Carlo techniques. Here we take the two-dimensional coupled $XY$-Ising model as an example. Furthermore, we calculate interface free energies of finite three-dimensional O($n$) models, for the three cases $n=1$, 2 and 3. Application of finite-size scaling to the numerical results yields estimates of the critical points of these three models. The statistical precision of the estimates is satisfactory for the modest amount of computer time spent

Magnetization reversal times in the 2D Ising model

We present a theoretical framework which is generally applicable to the study of time scales of activated processes in systems with Brownian type dynamics. This framework is applied to a prototype system: magnetization reversal times in the 2D Ising model. Direct simulation results for the magnetization reversal times, spanning more than five orders of magnitude, are compared with theoretical predictions; the two agree in most cases within 20%.Comment: 9 pages, 8 figure

Critical behavior of the frustrated antiferromagnetic six-state clock model on a triangular lattice

We study the anti-ferromagnetic six-state clock model with nearest neighbor interactions on a triangular lattice with extensive Monte-Carlo simulations. We find clear indications of two phase transitions at two different temperatures: Below $T_I$ a chirality order sets in and by a thorough finite size scaling analysis of the specific heat and the chirality correlation length we show that this transition is in the Ising universality class (with a non-vanishing chirality order parameter below $T_I$). At $T_{KT}(<T_I)$ the spin-spin correlation length as well as the spin susceptibility diverges according to a Kosterlitz-Thouless (KT) form and spin correlations decay algebraically below $T_{KT}$. We compare our results to recent x-ray diffraction experiments on the orientational ordering of CF$_3$Br monolayers physisorbed on graphite. We argue that the six-state clock model describes the universal feature of the phase transition in the experimental system and that the orientational ordering belongs to the KT universality class.Comment: 8 pages, 9 figure

Dynamics of Phase Transitions by Hysteresis Methods I

In studies of the QCD deconfining phase transition or crossover by means of heavy ion experiments, one ought to be concerned about non-equilibrium effects due to heating and cooling of the system. Motivated by this, we look at hysteresis methods to study the dynamics of phase transitions. Our systems are temperature driven through the phase transition using updating procedures in the Glauber universality class. Hysteresis calculations are presented for a number of observables, including the (internal) energy, properties of Fortuin-Kasteleyn clusters and structure functions. We test the methods for 2d Potts models, which provide a rich collection of phase transitions with a number of rigorously known properties. Comparing with equilibrium configurations we find a scenario where the dynamics of the transition leads to a spinodal decomposition which dominates the statistical properties of the configurations. One may expect an enhancement of low energy gluon production due to spinodal decomposition of the Polyakov loops, if such a scenario is realized by nature.Comment: 12 pages, revised after referee report, to appear in Phys. Rev.

On the Application of the Non Linear Sigma Model to Spin Chains and Spin Ladders

We review the non linear sigma model approach (NLSM) to spin chains and spin ladders, presenting new results. The generalization of the Haldane's map to ladders in the Hamiltonian approach, give rise to different values of the $\theta$ parameter depending on the spin S, the number of legs $n_{\ell}$ and the choice of blocks needed to built up the NLSM fields. For rectangular blocks we obtain $\theta = 0$ or $2 \pi S$ depending on wether $n_{\ell}$, is even or odd, while for diagonal blocks we obtain $\theta = 2 \pi S n_{\ell}$. Both results agree modulo $2 \pi$, and yield the same prediction, namely that even ( resp. odd) ladders are gapped (resp. gapless). For even legged ladders we show that the spin gap collapses exponentially with $n_{\ell}$ and we propose a finite size correction to the gap formula recently derived by Chakravarty using the 2+1 NSLM, which gives a good fit of numerical results. We show the existence of a Haldane phase in the two legged ladder using diagonal blocks and finally we consider the phase diagram of dimerized ladders.Comment: 25 pages, Latex, 7 figures in postscript files, Proc. of the 1996 El Escorial Summer School on "Strongly Correlated Magnetic and Superconducting Systems". Some more references are adde

Discriminating instance generation for automated constraint model selection

One approach to automated constraint modelling is to generate, and then select from, a set of candidate models. This method is used by the automated modelling system Conjure. To select a preferred model or set of models for a problem class from the candidates Conjure produces, we use a set of training instances drawn from the target class. It is important that the training instances are discriminating. If all models solve a given instance in a trivial amount of time, or if no models solve it in the time available, then the instance is not useful for model selection. This paper addresses the task of generating small sets of discriminating training instances automatically. The instance space is determined by the parameters of the associated problem class. We develop a number of methods of finding parameter configurations that give discriminating training instances, some of them leveraging existing parameter-tuning techniques. Our experimental results confirm the success of our approach in reducing a large set of input models to a small set that we can expect to perform well for the given problem class

Cosmological distance indicators

We review three distance measurement techniques beyond the local universe: (1) gravitational lens time delays, (2) baryon acoustic oscillation (BAO), and (3) HI intensity mapping. We describe the principles and theory behind each method, the ingredients needed for measuring such distances, the current observational results, and future prospects. Time delays from strongly lensed quasars currently provide constraints on $H_0$ with < 4% uncertainty, and with 1% within reach from ongoing surveys and efforts. Recent exciting discoveries of strongly lensed supernovae hold great promise for time-delay cosmography. BAO features have been detected in redshift surveys up to z <~ 0.8 with galaxies and z ~ 2 with Ly-$\alpha$ forest, providing precise distance measurements and $H_0$ with < 2% uncertainty in flat $\Lambda$CDM. Future BAO surveys will probe the distance scale with percent-level precision. HI intensity mapping has great potential to map BAO distances at z ~ 0.8 and beyond with precisions of a few percent. The next years ahead will be exciting as various cosmological probes reach 1% uncertainty in determining $H_0$, to assess the current tension in $H_0$ measurements that could indicate new physics.Comment: Review article accepted for publication in Space Science Reviews (Springer), 45 pages, 10 figures. Chapter of a special collection resulting from the May 2016 ISSI-BJ workshop on Astronomical Distance Determination in the Space Ag

Deficiências minerais em plantas de bertalha ( Basella alba, L.)

Basella alba is used as a major food on the Amazon region, north Brazil for its high mineral and vitamins content. The purpose of the present work was: a) obtain a clear picture of the macronutrient deficiency; b) growth of the plants in function of (1); c) analyptical levels found in the leaves. Young Basella alba plants (bertalha in Portuguese) were cultivated in pots containing fine pure quartz and irrigated by percolation with different nutrient solutions lacking one of the element at the time. Clear cut symptoms were obtained for all macronutrients. Only the omission of nitrogen and potassium affect the dry matter production of plants. The range in dry matter for unhealthy and healthy leaves were: N% = 1.25--3-55; P% = 0.17-0.36; K% = 0.46-3.55; Ca% = 0,62-1.78; Mg% = 0.37-0.80; S% = 0.19-0.13.Plantas de bertalha (Basella alba, L.) INPA-1 foram cultivadas em casa de vegetação em quartzo moído, irrigadas com soluções nutritivas conforme SARRUGE (1975) e submetidas aos seguintes tratamentos: completo, omissão de N, omissão de P, omissão de K, omissão de Ca, omissão de Mg e omissão de S, com o objetivo de: (a) obter sintomas de deficiência dos ma cronutrientes; (b) analisar o crescimento das plantas através da produção de matéria seca; (c) determinar a concentração dos macronutrientes nas folhas e caules das plantas cultivadas nos diversos tratamentos. Os sintomas visuais de deficiência foram identificados e descritos. As plantas foram coletadas e separadas em raiz, caule, folhas e determinaram-se os teores dos macronutrientes minerais neste material. Os resultados obtidos mostram: - os sintomas visuais de deficiência são bem definidos e de fácil caracterização para todos os nutrientes; - só foi possível detectar efeito na produção de matéria seca das folhas e caules para omissão de nitrogênio e para omissão de potássio nos caules; - os níveis de deficiência e adequação obtidos nas folhas foram respectivamente: N% = 1,25 e 2,63; P% = 0,17 e 0,36; K% = 0,46 e 3,55; Ca% = 0,62e 1,78; Mg% = 0,37 e 0,80; s%= 0,19 e 0,23. - os níveis de deficiência e adequação obtidos nos caules foram respectivamente: N% = 0,67 e 0,98; P% = 0,13 e 0,31; K% = 0,73 e 2,67; Ca% = 0,11 e 0,64; Mg% = 0,08 e 0,20; S% = 0,15 e 0,20