Geometrical mutual information at the tricritical point of the two-dimensional Blume-Capel model

The spin-1 classical Blume-Capel model on a square lattice is known to exhibit a finite-temperature phase transition described by the tricritical Ising CFT in 1+1 space-time dimensions. This phase transition can be accessed with classical Monte Carlo simulations, which, via a replica-trick calculation, can be used to study the shape-dependence of the classical R\'enyi entropies for a torus divided into two cylinders. From the second R\'enyi entropy, we calculate the Geometrical Mutual Information (GMI) introduced by St\'ephan et. al. [Phys. Rev. Lett. 112, 127204 (2014)] and use it to extract a numerical estimate for the value of the central charge near the tricritical point. By comparing to the known CFT result, $c=7/10$, we demonstrate how this type of GMI calculation can be used to estimate the position of the tricritical point in the phase diagram.Comment: version accepted in JSTA

RVB gauge theory and the Topological degeneracy in the Honeycomb Kitaev model

We relate the Z$_2$ gauge theory formalism of the Kitaev model to the SU(2) gauge theory of the resonating valence bond (RVB) physics. Further, we reformulate a known Jordan-Wigner transformation of Kitaev model on a torus in a general way that shows that it can be thought of as a Z$_2$ gauge fixing procedure. The conserved quantities simplify in terms of the gauge invariant Jordan-Wigner fermions, enabling us to construct exact eigen states and calculate physical quantities. We calculate the fermionic spectrum for flux free sector for different gauge field configurations and show that the ground state is four-fold degenerate on a torus in thermodynamic limit. Further on a torus we construct four mutually anti-commuting operators which enable us to prove that all eigenstates of this model are four fold degenerate in thermodynamic limit.Comment: 12 pages, 3 figures. Added affiliation and a new section, 'Acknowledgements'.Typos correcte

Exactly solvable Kitaev model in three dimensions

We introduce a spin-1/2 model in three dimensions which is a generalization of the well-known Kitaev model on a honeycomb lattice. Following Kitaev, we solve the model exactly by mapping it to a theory of non-interacting fermions in the background of a static Z_2 gauge field. The phase diagram consists of a gapped phase and a gapless one, similar to the two-dimensional case. Interestingly, unlike in the two-dimensional model, in the gapless phase the gap vanishes on a contour in the k space. Furthermore, we show that the flux excitations of the gauge field, due to some local constraints, form loop like structures; such loops exist on a lattice formed by the plaquettes in the original lattice and is topologically equivalent to the pyrochlore lattice. Finally, we derive a low-energy effective Hamiltonian that can be used to study the properties of the excitations in the gapped phase.Comment: 9 pages, 7 figures; published version; a new section and more references adde

Development of sustainable aquaculture project (DSAP): mid-term review report

Aquaculture, Fish culture, Pond Culture, Rice field aquaculture, Farmers, Bangladesh,

Evolution of hydromagnetic turbulence from the electroweak phase transition

We present new simulations of decaying hydromagnetic turbulence for a relativistic equation of state relevant to the early universe. We compare helical and nonhelical cases either with kinetically or magnetically dominated initial fields. Both kinetic and magnetic initial helicities lead to maximally helical magnetic fields after some time, but with different temporal decay laws. Both are relevant to the early universe, although no mechanisms have yet been identified that produce magnetic helicity with strengths comparable to the big bang nucleosynthesis limit at scales comparable to the Hubble horizon at the electroweak phase transition. Nonhelical magnetically dominated fields could still produce picoGauss magnetic fields under most optimistic conditions. Only helical magnetic fields can potentially have nanoGauss strengths at scales up to 30 kpc today.Comment: 17 pages, 13 figures; submitted to PR

Distinguishing Posed and Spontaneous Smiles by Facial Dynamics

Smile is one of the key elements in identifying emotions and present state of mind of an individual. In this work, we propose a cluster of approaches to classify posed and spontaneous smiles using deep convolutional neural network (CNN) face features, local phase quantization (LPQ), dense optical flow and histogram of gradient (HOG). Eulerian Video Magnification (EVM) is used for micro-expression smile amplification along with three normalization procedures for distinguishing posed and spontaneous smiles. Although the deep CNN face model is trained with large number of face images, HOG features outperforms this model for overall face smile classification task. Using EVM to amplify micro-expressions did not have a significant impact on classification accuracy, while the normalizing facial features improved classification accuracy. Unlike many manual or semi-automatic methodologies, our approach aims to automatically classify all smiles into either `spontaneous' or `posed' categories, by using support vector machines (SVM). Experimental results on large UvA-NEMO smile database show promising results as compared to other relevant methods.Comment: 16 pages, 8 figures, ACCV 2016, Second Workshop on Spontaneous Facial Behavior Analysi

A Note on D-Branes of Odd Codimensions from Noncommutative Tachyons

On a noncommutative space of rank-1, we construct a codimension-one soliton explicitly and, in the context of noncommutative bosonic open string theory, identify it with the D24-brane. We compute the tension of the proposed D24-brane, yielding an exact value and show that it is related to the tension of the codimension two D23-brane by the string T-duality. This resolves a puzzle posed by the result of Harvey, Kraus, Larsen and Martinec. We also apply the result to non-BPS branes in superstring theories and argue that the codimension-one soliton gives rise to new descent relation among the non-BPS branes in Type IIA and Type IIB string theories via T-duality

Chiral Properties of QCD Vacuum in Magnetars- A Nambu-Jona-Lasinio Model with Semi-Classical Approximation

The breaking of chiral symmetry of light quarks at zero temperature in presence of strong quantizing magnetic fiels is studied using Nambu-Jona-Lasinio (NJL) model with Thomas-Fermi type semi-classical formalism. It is found that the dynamically generated light quark mass can never become zero if the Landau levels are populated and the mass increases with the increase of magnetic field strength.Comment: REVTEX 11 Pages, One .eps figure (included

Spin analog of the controlled Josephson charge current

We propose a controlled Josephson spin current across the junction of two non-centrosymmetric superconductors like CePt_3Si. The Josephson spin current arises due to direction dependent tunneling matrix element and different momentum dependent phases of the triplet components of the gap function. Its modulation with the angle \xi between the noncentrosymmetric axes of two superconductors is proportional to \sin \xi. This particular dependence on \xi may find application of the proposed set-up in making a Josephson spin switch.Comment: 4 pages, 1 figure; title is changed; article is rewritte