Curves on threefolds and a conjecture of Griffiths-Harris

We prove that any arithmetically Gorenstein curve on a smooth, general hypersurface of degree at least 6, is a complete intersection. This gives a characterisation of complete intersection curves on general type hypersurfaces in . We also verify that certain 1-cycles on a general quintic hypersurface are non-trivial elements of the Griffiths group.

Thomas-Fermi Method For Particles Obeying Generalized Exclusion Statistics

We use the Thomas-Fermi method to examine the thermodynamics of particles obeying Haldane exclusion statistics. Specifically, we study Calogero-Sutherland particles placed in a given external potential in one dimension. For the case of a simple harmonic potential (constant density of states), we obtain the exact one-particle spatial density and a {\it closed} form for the equation of state at finite temperature, which are both new results. We then solve the problem of particles in a $x^{2/3} ~$ potential (linear density of states) and show that Bose-Einstein condensation does not occur for any statistics other than bosons.

Griffiths phase-like behavior and spin-phonon coupling in double perovskite Tb(2)NiMnO(6)

The Griffiths phase-like features and the spin-phonon coupling effects observed in Tb(2)NiMnO(6) are reported. The double perovskite compound crystallizes in monoclinic P2(1)/n space group and exhibits a magnetic phase transition at T(c) similar to 111 K as an abrupt change in magnetization. A negative deviation from ideal Curie-Weiss law exhibited by 1/chi(T) curves and less-than-unity susceptibility exponents from the power-law analysis of inverse susceptibility are reminiscent of Griffiths phase-like features. Arrott plots derived from magnetization isotherms support the inhomogeneous nature of magnetism in this material. The observed effects originate from antiferromagnetic interactions that arise from inherent disorder in the system. Raman scattering experiments display no magnetic-order-induced phonon renormalization below Tc in Tb(2)NiMnO(6), which is different from the results observed in other double perovskites and is correlated to the smaller size of the rare earth. The temperature evolution of full-width-at-half-maximum for the stretching mode at 645 cm(-1) presents an anomaly that coincides with the magnetic transition temperature and signals a close connection between magnetism and lattice in this material. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3671674]

Glassy dielectric response in Tb2NiMnO6 double perovskite with similarities to a Griffiths phase

Results of frequency-dependent and temperature-dependent dielectric measurements performed on the double-perovskite Tb2NiMnO6 are presented. The real (epsilon(1)(f,T)) and imaginary (epsilon(2)(f,T)) parts of dielectric permittivity show three plateaus suggesting dielectric relaxation originating from the bulk, grain boundaries and the sample-electrode interfaces, respectively. The epsilon(1)(f,T) and epsilon(2)(f,T) are successfully simulated by a RC circuit model. The complex plane of impedance, Z'-Z `', is simulated using a series network with a resistor R and a constant phase element. Through the analysis of epsilon(f,T) using the modified Debye model, two different relaxation time regimes separated by a characteristic temperature, T*, are identified. The temperature variation of R and C corresponding to the bulk and the parameter alpha from modified Debye fit lend support to this hypothesis. Interestingly, the T* compares with the Griffiths temperature for this compound observed in magnetic measurements. Though these results cannot be interpreted as magnetoelectric coupling, the relationship between lattice and magnetism is markedly clear. We assume that the observed features have their origin in the polar nanoregions which originate from the inherent cationic defect structure of double perovskites. Copyright (C) EPLA, 2013