Prospect of common effluent treatment plant (CETP) in industrial sector

Prospect of common effluent treatment plant (CETP) in industrial secto

Probing a ferromagnetic critical regime using nonlinear susceptibility

The second order para-ferromagnetic phase transition in a series of amorphous alloys (Fe{_5}Co{_{50}}Ni{_{17-x}}Cr{_x}B{_{16}}Si{_{12}}) is investigated using nonlinear susceptibility. A simple molecular field treatment for the critical region shows that the third order suceptibility (chi{_3}) diverges on both sides of the transition temperature, and changes sign at T{_C}. This critical behaviour is observed experimentally in this series of amorphous ferromagnets, and the related assymptotic critical exponents are calculated. It is shown that using the proper scaling equations, all the exponents necessary for a complete characterization of the phase transition can be determined using linear and nonlinear susceptiblity measurements alone. Using meticulous nonlinear susceptibility measurements, it is shown that at times chi{_3} can be more sensitive than the linear susceptibility (chi{_1}) in unravelling the magnetism of ferromagnetic spin systems. A new technique for accurately determining T{_C} is discussed, which makes use of the functional form of chi{_3} in the critical region.Comment: 11 Figures, Submitted to Physical Review

Algebraic approach to quantum black holes: logarithmic corrections to black hole entropy

The algebraic approach to black hole quantization requires the horizon area eigenvalues to be equally spaced. As shown previously, for a neutral non-rotating black hole, such eigenvalues must be $2^{n}$-fold degenerate if one constructs the black hole stationary states by means of a pair of creation operators subject to a specific algebra. We show that the algebra of these two building blocks exhibits $U(2)\equiv U(1)\times SU(2)$ symmetry, where the area operator generates the U(1) symmetry. The three generators of the SU(2) symmetry represent a {\it global} quantum number (hyperspin) of the black hole, and we show that this hyperspin must be zero. As a result, the degeneracy of the $n$-th area eigenvalue is reduced to $2^{n}/n^{3/2}$ for large $n$, and therefore, the logarithmic correction term $-3/2\log A$ should be added to the Bekenstein-Hawking entropy. We also provide a heuristic approach explaining this result, and an evidence for the existence of {\it two} building blocks.Comment: 15 pages, Revtex, to appear in Phys. Rev.

Spin Fluctuations and the Magnetic Phase Diagram of ZrZn2

The magnetic properties of the weak itinerant ferromagnet ZrZn_2 are analyzed using Landau theory based on a comparison of density functional calculations and experimental data as a function of field and pressure. We find that the magnetic properties are strongly affected by the nearby quantum critical point, even at zero pressure; LDA calculations neglecting quantum critical spin fluctuations overestimate the magnetization by a factor of approximately three. Using renormalized Landau theory, we extract pressure dependence of the fluctuation amplitude. It appears that a simple scaling based on the fluctuation-dissipation theorem provides a good description of this pressure dependence.Comment: 4 revtex page

Logarithmic Corrections to Rotating Extremal Black Hole Entropy in Four and Five Dimensions

We compute logarithmic corrections to the entropy of rotating extremal black holes using quantum entropy function i.e. Euclidean quantum gravity approach. Our analysis includes five dimensional supersymmetric BMPV black holes in type IIB string theory on T^5 and K3 x S^1 as well as in the five dimensional CHL models, and also non-supersymmetric extremal Kerr black hole and slowly rotating extremal Kerr-Newmann black holes in four dimensions. For BMPV black holes our results are in perfect agreement with the microscopic results derived from string theory. In particular we reproduce correctly the dependence of the logarithmic corrections on the number of U(1) gauge fields in the theory, and on the angular momentum carried by the black hole in different scaling limits. We also explain the shortcomings of the Cardy limit in explaining the logarithmic corrections in the limit in which the (super)gravity description of these black holes becomes a valid approximation. For non-supersymmetric extremal black holes, e.g. for the extremal Kerr black hole in four dimensions, our result provides a stringent testing ground for any microscopic explanation of the black hole entropy, e.g. Kerr/CFT correspondence.Comment: LaTeX file, 50 pages; v2: added extensive discussion on the relation between boundary condition and choice of ensemble, modified analysis for slowly rotating black holes, all results remain unchanged, typos corrected; v3: minor additions and correction

Magnetic relaxation phenomena and cluster glass properties of La{0.7-x}Y{x}Ca{0.3}MnO{3} manganites

The dynamic magnetic properties of the distorted perovskite system La{0.7-x}Y{x}Ca{0.3}MnO{3} (0 <= x <= 0.15) have been investigated by ac-susceptibility and dc magnetization measurements, with emphasis on relaxation and aging studies. They evidence for x >= 0.10 the appearance of a metallic cluster glass phase, that develops just below the ferromagnetic transition temperature. The clusters grow with decreasing temperature down to a temperature T(f0) at which they freeze due to severe intercluster frustration. The formation of these clusters is explained by the presence of yttrium induced local structural distortions that create localized spin disorder in a magnetic lattice where double-exchange ferromagnetism is dominant.Comment: Accepted for publication in Phys. Rev.

Magnetism, Critical Fluctuations and Susceptibility Renormalization in Pd

Some of the most popular ways to treat quantum critical materials, that is, materials close to a magnetic instability, are based on the Landau functional. The central quantity of such approaches is the average magnitude of spin fluctuations, which is very difficult to measure experimentally or compute directly from the first principles. We calculate the parameters of the Landau functional for Pd and use these to connect the critical fluctuations beyond the local-density approximation and the band structure.Comment: Replaced with the revised version accepted for publication. References updated, errors corrected, other change

Logarithmic Corrections to N=2 Black Hole Entropy: An Infrared Window into the Microstates

Logarithmic corrections to the extremal black hole entropy can be computed purely in terms of the low energy data -- the spectrum of massless fields and their interaction. The demand of reproducing these corrections provides a strong constraint on any microscopic theory of quantum gravity that attempts to explain the black hole entropy. Using quantum entropy function formalism we compute logarithmic corrections to the entropy of half BPS black holes in N=2 supersymmetric string theories. Our results allow us to test various proposals for the measure in the OSV formula, and we find agreement with the measure proposed by Denef and Moore if we assume their result to be valid at weak topological string coupling. Our analysis also gives the logarithmic corrections to the entropy of extremal Reissner-Nordstrom black holes in ordinary Einstein-Maxwell theory.Comment: LaTeX file, 66 page

Critical exponents and equation of state of the three-dimensional Heisenberg universality class

We improve the theoretical estimates of the critical exponents for the three-dimensional Heisenberg universality class. We find gamma=1.3960(9), nu=0.7112(5), eta=0.0375(5), alpha=-0.1336(15), beta=0.3689(3), and delta=4.783(3). We consider an improved lattice phi^4 Hamiltonian with suppressed leading scaling corrections. Our results are obtained by combining Monte Carlo simulations based on finite-size scaling methods and high-temperature expansions. The critical exponents are computed from high-temperature expansions specialized to the phi^4 improved model. By the same technique we determine the coefficients of the small-magnetization expansion of the equation of state. This expansion is extended analytically by means of approximate parametric representations, obtaining the equation of state in the whole critical region. We also determine a number of universal amplitude ratios.Comment: 40 pages, final version. In publication in Phys. Rev.

Higher order WKB corrections to black hole entropy in brick wall formalism

We calculate the statistical entropy of a quantum field with an arbitrary spin propagating on the spherical symmetric black hole background by using the brick wall formalism at higher orders in the WKB approximation. For general spins, we find that the correction to the standard Bekenstein-Hawking entropy depends logarithmically on the area of the horizon. Furthermore, we apply this analysis to the Schwarzschild and Schwarzschild-AdS black holes and discuss our results.Comment: 21 pages, published versio