Quantum phase transitions in a new exactly solvable quantum spin biaxial model with multiple spin interactions

The new integrable quantum spin model is proposed. The model has a biaxial magnetic anisotropy of alternating coupling between spins together with multiple spin interactions. Our model gives the possibility to exactly find thermodynamic characteristics of the considered spin chain. The ground state of the model can reveal spontaneous values of the total magnetic and antiferromagnetic moments, caused by multiple spin couplings. Also, in the ground state, depending on the strength of multiple spin couplings, our model manifests several quantum critical points, some of which are governed by the external magnetic field

Acoustic Cyclotron Resonance and Giant High Frequency Magnetoacoustic Oscillations in Metals with Locally Flattened Fermi Surface

We consider the effect of local flattening on the Fermi surface (FS) of a metal upon geometric oscillations of the velocity and attenuation of ultrasonic waves in the neighborhood of the acoustic cyclotron resonance. It is shown that such peculiarities of the local geometry of the FS can lead to a significant enhancement of both cyclotron resonance and geometric oscillations. Characteristic features of the coupling of ultrasound to shortwave cyclotron waves arising due to the local flattening of the FS are analyzed. PACS numbers 71.18.+y; 72.15.Gd; 72.15.-vComment: 8 pages, 3 figures, text revise

The ground state properties of the spin-1/2 transverse Ising chain with periodically varying bonds and fields

Using continued fractions we study the ground state properties of the spin-1/2 Ising chain in a transverse field with periodically varying interaction strengths and external fields. We consider in detail the chain having the period of modulation of interactions equals 2 and compare the results obtained with those corresponding to the spin-1/2 isotropic XY chain in a transverse field. In contrast to the behaviour of the transverse XY chain, the transverse Ising chain does not exhibit a step-like magnetization vs. field dependence caused by the alternation of bonds, its susceptibility exhibits a logarithmic singularity at the field determined by interaction strengths, and it is stable with respect to spin-Peierls dimerization.Comment: 11 pages, latex, 4 figure

Stationary Kolmogorov Solutions of the Smoluchowski Aggregation Equation with a Source Term

In this paper we show how the method of Zakharov transformations may be used to analyze the stationary solutions of the Smoluchowski aggregation equation for arbitrary homogeneous kernel. The resulting massdistributions are of Kolmogorov type in the sense that they carry a constant flux of mass from small masses to large. We derive a ``locality criterion'', expressed in terms of the asymptotic properties of the kernel, that must be satisfied in order for the Kolmogorov spectrum to be an admissiblesolution. Whether a given kernel leads to a gelation transition or not can be determined by computing the mass capacity of the Kolmogorov spectrum. As an example, we compute the exact stationary state for the family of kernels,$K_\zeta(m_1,m_2)=(m_1m_2)^{\zeta/2}$ which includes both gelling and non-gelling cases, reproducing the known solution in the case $\zeta=0$. Surprisingly, the Kolmogorov constant is the same for all kernels in this family.Comment: This article is an expanded version of a talk given at IHP workshop "Dynamics, Growth and Singularities of Continuous Media", Paris July 2003. Updated 01/04/04. Revised version with additional discussion, references added, several typographical errors corrected. Revised version accepted for publication by Phys. Rev.

Dynamics of Vortex Pair in Radial Flow

The problem of vortex pair motion in two-dimensional plane radial flow is solved. Under certain conditions for flow parameters, the vortex pair can reverse its motion within a bounded region. The vortex-pair translational velocity decreases or increases after passing through the source/sink region, depending on whether the flow is diverging or converging, respectively. The rotational motion of two corotating vortexes in a quiescent environment transforms into motion along a logarithmic spiral in the presence of radial flow. The problem may have applications in astrophysics and geophysics.Comment: 13 pages, 9 figure

New symmetries of the chiral Potts model

In this paper a hithertho unknown symmetry of the three-state chiral Potts model is found consisting of two coupled Temperley-Lieb algebras. From these we can construct new superintegrable models. One realisation is in terms of a staggered isotropic XY spin chain. Further we investigate the importance of the algebra for the existence of mutually commuting charges. This leads us to a natural generalisation of the boost-operator, which generates the charges.Comment: 19 pages, improved notation, made the text easier to read, corrected some typo

A Dipole Vortex Model of Obscuring Tori in Active Galaxy Nuclei

The torus concept as an essential structural component of active galactic nuclei (AGN) is generally accepted. Here, the situation is discussed when the torus "twisting" by the radiation or wind transforms it into a dipole toroidal vortex which in turn can be a source of matter replenishing the accretion disk. Thus emerging instability which can be responsible for quasar radiation flares accompanied by matter outbursts is also discussed. The "Matreshka" scheme for an obscuring vortex torus structure capable of explaining the AGN variability and evolution is proposed. The model parameters estimated numerically for the luminosity close to the Eddington limit agree well with the observations.Comment: 17 pages, 11 figures, version of this paper is published in Astronomy Report

Hydrodynamic Detonation Instability in Electroweak and QCD Phase Transitions

The hydrodynamic stability of deflagration and detonation bubbles for a first order electroweak and QCD phase transition has been discussed recently with the suggestion that detonations are stable. We examine here the case of a detonation more carefully. We find that in front of the bubble wall perturbations do not grow with time, but behind the wall modes exist which grow exponentially. We briefly discuss the possible meaning of this instability.Comment: 12 pages, 3 figures available on request, Latex, FERMILAB--PUB--93/098--