A solvable quantum antiferromagnet model

We introduce a quantum antiferromagnet model, having exactly soluble thermodynamic properties. It is an infinite range antiferromagnetic Ising model put in a transverse field. The free energy gives the ground state energy in the zero temperature limit and it also gives the low temperature behaviour of the specific heat, the exponential variation of which gives the precise gap magnitude in the excitation spectrum of the system. The detailed behaviour of the (random sublattice) staggard magnetisation and susceptibilities are obtained and studied near the N\'eel temperature and the zero temperature quantum critical point.Comment: 4 pages, 2 eps figure

Quantum phase transition in a disordered long-range transverse Ising antiferromagnet

We consider a long-range Ising antiferromagnet put in a transverse field (LRTIAF) with disorder. We have obtained the phase diagrams for both the classical and quantum case. For the pure case applying quantum Monte Carlo method, we study the variation of order parameter (spin correlation in the Trotter direction), susceptibility and average energy of the system for various values of the transverse field at different temperatures. The antiferromagnetic order is seen to get immediately broken as soon as the thermal or quantum fluctuations are added. We discuss generally the phase diagram for the same LRTIAF model with perturbative Sherrington-Kirkpatrick (SK) type disorder. We find that while the antiferromagnetic order is immediately broken as one adds an infinitesimal transverse field or thermal fluctuation to the pure LRTIAF system, an infinitesimal SK spin glass disorder is enough to induce a stable glass order in the LRTIAF. This glass order eventually gets destroyed as the thermal or quantum fluctuations are increased beyond their threshold values and the transition to para phase occurs. Analytical studies for the phase transitions are discussed in detail in each case. These transitions have been confirmed by applying classical and quantum Monte Carlo methods. We show here that the disordered LRTIAF has a surrogate incubation property of the SK spin glass phase.Comment: 16 pages, 12 figures. accepted in PR

Do Water Fountain Jets Really Indicate the Onset of the Morphological Metamorphosis of Circumstellar Envelopes?

The small-scale bipolar jets having short dynamical ages from "water fountain (WF)" sources are regarded as an indication of the onset of circumstellar envelope morphological metamorphosis of intermediate-mass stars. Such process usually happens at the end of the asymptotic giant branch (AGB) phase. However, recent studies found that WFs could be AGB stars or even early planetary nebulae. This fact prompted the idea that WFs may not necessarily be objects at the beginning of the morphological transition process. In the present work, we show that WFs could have different envelope morphologies by studying their spectral energy distribution profiles. Some WFs have spherical envelopes that resembles usual AGB stars, while others have aspherical envelopes which are more common to post-AGB stars. The results imply that WFs may not represent the earliest stage of the morphological metamorphosis. We further argue that the dynamical age of a WF jet, which can be calculated from maser proper motions, may not be the real age of the jet. The dynamical age cannot be used to justify the moment when the envelope begins to become aspherical, nor to tell the concrete evolutionary status of the object. A WF jet could be the innermost part of a larger well-developed jet, which is not necessarily a young jet.Comment: 21 pages, 4 figures, accepted for publication in MNRA

4p states and X-Ray Spectroscopy

The 4p states in transition metals and their compounds usually play minor roles on their physical quantities. Recent development of resonant x-ray scattering (RXS) at the K-edge of transition metals, however, casts light on the 4p states, because the signals on orbital and magnetic superlattice spots are brought about by the modulation in the 4p states. The 4p states are extending in solids and thereby sensitive to electronic states at neighboring sites. This characteristic determines the mechanism of RXS that the intensity on the orbital superlattice spots are mainly generated by the lattice distortion and those on magnetic superlattice spots by the coupling of the 4p states with the orbital polarization in the 3d states at neighboring sites. Taking up typical examples for orbital and magnetic RXS, we demonstrate these mechanisms on the basis of the band structure calculation. Finally, we study the MCD spectra at the K-edge, demonstrating that the same mechanism as the magnetic RXS is working.Comment: 9 pages, 9 figures, submitted to Physica Scripta (comment

Log-aesthetic Curves as Similarity Geometric Analogue of Euler's Elasticae

In this paper we consider the log-aesthetic curves and their generalization which are used in CAGD. We consider those curves under similarity geometry and characterize them as stationary integrable flow on plane curves which is governed by the Burgers equation. We propose a variational formulation of those curves whose Euler-Lagrange equation yields the stationary Burgers equation. Our result suggests that the log-aesthetic curves and their generalization can be regarded as the similarity geometric analogue of Euler's elasticae