Multidimensional persistence behaviour in an Ising system

We consider a periodic Ising chain with nearest-neighbour and $r$-th neighbour interaction and quench it from infinite temperature to zero temperature. The persistence probability $P(t)$, measured as the probability that a spin remains unflipped upto time $t$, is studied by computer simulation for suitable values of $r$. We observe that as time progresses, $P(t)$ first decays as $t^{-0.22}$ (-the {\em first} regime), then the $P(t)-t$ curve has a small slope (in log-log scale) for some time (-the {\em second} regime) and at last it decays nearly as $t^{-3/8}$ (-the {\em third} regime). We argue that in the first regime, the persistence behaviour is the usual one for a two-dimensional system, in the second regime it is like that of a non-interacting (`zero-dimensional') system and in the third regime the persistence behaviour is like that of a one dimensional Ising model. We also provide explanations for such behaviour.Comment: 6 pages, 12 figure

A Small World Network of Prime Numbers

According to Goldbach conjecture, any even number can be broken up as the sum of two prime numbers : $n = p + q$. We construct a network where each node is a prime number and corresponding to every even number $n$, we put a link between the component primes $p$ and $q$. In most cases, an even number can be broken up in many ways, and then we chose {\em one} decomposition with a probability $|p - q|^{\alpha}$. Through computation of average shortest distance and clustering coefficient, we conclude that for $\alpha > -1.8$ the network is of small world type and for $\alpha < -1.8$ it is of regular type. We also present a theoretical justification for such behaviour.Comment: 6 pages, 10 figure

Changing trends of maternal mortality with its causes- ten years retrospective study in a peripheral medical college of West Bengal, India

Background: The estimates of maternal mortality can only be used as a rough indicator of maternal health situation in any given country. High maternal mortality reflects not only in inadequacy of health care services for mothers, but also a low standard of living and socio economic status of the community. Objective was to assess the maternal mortality ratio (MMR), its probable causes and changing trends.Methods: The present study conducted at Midnapore Medical College (MMC), West Bengal. Data for analysis were collected from medical college record section and maternal death registrar book after having permission from higher authority of the college during the period from January 2009 to 2018 December. Total sample size for this period was 249. Statistical analysis was done through SPSS software.Results: Ten years data analysis of 249 subjects showed that total live births from January 2009 to December 2018 was 1,39,126 with MMR 178.97%. Hypertensive disorder of pregnancy (40.56%) was the leading direct cause of maternal death followed by hemorrhage (24.49%) and septicemia (10.84%). Heart disease (6.42%) was the major indirect cause of death followed by anemia (3.6%). Maternal death rate found high among primi gravida (59.43%) mothers and within 20 years age group (46.18%).Conclusions: Most maternal deaths are preventable by proper antenatal care, early diagnosis of high risk factors, timely referral to tertiary care centre along with community upliftment especially in rural and tribal based population.

Floating Phase in 1D Transverse ANNNI Model

To study the ground state of ANNNI chain under transverse field as a function of frustration parameter $\kappa$ and field strength $\Gamma$, we present here two different perturbative analyses. In one, we consider the (known) ground state at $\kappa=0.5$ and $\Gamma=0$ as the unperturbed state and treat an increase of the field from 0 to $\Gamma$ coupled with an increase of $\kappa$ from 0.5 to $0.5+r\Gamma$ as perturbation. The first order perturbation correction to eigenvalue can be calculated exactly and we could conclude that there are only two phase transition lines emanating from the point $\kappa=0.5$, $\Gamma=0$. In the second perturbation scheme, we consider the number of domains of length 1 as the perturbation and obtain the zero-th order eigenfunction for the perturbed ground state. From the longitudinal spin-spin correlation, we conclude that floating phase exists for small values of transverse field over the entire region intermediate between the ferromagnetic phase and antiphase.Comment: 11 pages, 11 figure