Proper Matter Collineations of Plane Symmetric Spacetimes

We investigate matter collineations of plane symmetric spacetimes when the energy-momentum tensor is degenerate. There exists three interesting cases where the group of matter collineations is finite-dimensional. The matter collineations in these cases are either four, six or ten in which four are isometries and the rest are proper.Comment: 10 pages, LaTex, accepted for publication in Modern Physics Letters

The Association between Mercury Emissions and Individuals with Autism Aged from 3-21 in the State of California from 2001 to 2007

The paper explores how historical mercury deposition associates with the incidents of autism, identified in individuals aged from 3 to 21 in California from 2001 to 2007. The association between mercury deposits and the prevalence of individuals with autism aged from 3 to 21 in California was explored using the data from the National Atmospheric Deposition Program and the U.S. Education Department. A correlation analysis is applied to find if a relationship between mercury deposits and the autistic individuals in California. A regression test is run showing that for every 2.41ng/square meter per year increase of mercury deposits in California, there is a corresponding 3.55 person increase of autistic individuals aged from 3 to 21 historically from 2001 to 2007. Due to constraint factors in the research (please see the conclusion section), the comparison study did not show a statistically significant difference but the study indicated the importance of examining the effect of environmental toxins and their impact on human health

Phase transitions in the frustrated Ising model on the square lattice

We consider the thermal phase transition from a paramagnetic to stripe-antiferromagnetic phase in the frustrated two-dimensional square-lattice Ising model with competing interactions J1<0 (nearest neighbor, ferromagnetic) and J2 >0 (second neighbor, antiferromagnetic). The striped phase breaks a Z4 symmetry and is stabilized at low temperatures for g=J2/|J1|>1/2. Despite the simplicity of the model, it has proved difficult to precisely determine the order and the universality class of the phase transitions. This was done convincingly only recently by Jin et al. [PRL 108, 045702 (2012)]. Here, we further elucidate the nature of these transitions and their anomalies by employing a combination of cluster mean-field theory, Monte Carlo simulations, and transfer-matrix calculations. The J1-J2 model has a line of very weak first-order phase transitions in the whole region 1/2<g<g*, where g* = 0.67(1). Thereafter, the transitions from g above g* are continuous and can be fully mapped, using universality arguments, to the critical line of the well known Ashkin-Teller model from its 4-state Potts point to the decoupled Ising limit. We also comment on the pseudo-first-order behavior at the Potts point and its neighborhood in the Ashkin-Teller model on finite lattices, which in turn leads to the appearance of similar effects in the vicinity of the multicritical point g* in the J1-J2 model. The continuous transitions near g* can therefore be mistaken to be first-order transitions, and this realization was the key to understanding the paramagnetic-striped transition for the full range of g>1/2. Most of our results are based on Monte Carlo calculations, while the cluster mean-field and transfer-matrix results provide useful methodological bench-marks for weakly first-order behaviors and Ashkin-Teller criticality.Comment: 13 pages, 13 figure

Parametrization of Quintessence and Its Potential

We develop a theoretical method of constructing the quintessence potential directly from the effective equation of state function $w(z)$, which describes the properties of the dark energy. We apply our method to four parametrizations of equation of state parameter and discuss the general features of the resulting potentials. In particular, it is shown that the constructed quintessence potentials are all in the form of a runaway type.Comment: 6 pages, 2 figures, LaTeX2