Spin-spin Correlation in Some Excited States of Transverse Ising Model

We consider the transverse Ising model in one dimension with nearest-neighbour interaction and calculate exactly the longitudinal spin-spin correlation for a class of excited states. These states are known to play an important role in the perturbative treatment of one-dimensional transverse Ising model with frustrated second-neighbour interaction. To calculate the correlation, we follow the earlier procedure of Wu, use Szego's theorem and also use Fisher-Hartwig conjecture. The result is that the correlation decays algebraically with distance ($n$) as $1/\surd n$ and is oscillatory or non-oscillatory depending on the magnitude of the transverse field.Comment: 5 pages, 1 figur

Exact renormalization of the random transverse-field Ising spin chain in the strongly ordered and strongly disordered Griffiths phases

The real-space renormalization group (RG) treatment of random transverse-field Ising spin chains by Fisher ({\it Phys. Rev. B{\bf 51}, 6411 (1995)}) has been extended into the strongly ordered and strongly disordered Griffiths phases and asymptotically exact results are obtained. In the non-critical region the asymmetry of the renormalization of the couplings and the transverse fields is related to a non-linear quantum control parameter, $\Delta$, which is a natural measure of the distance from the quantum critical point. $\Delta$, which is found to stay invariant along the RG trajectories and has been expressed by the initial disorder distributions, stands in the singularity exponents of different physical quantities (magnetization, susceptibility, specific heat, etc), which are exactly calculated. In this way we have observed a weak-universality scenario: the Griffiths-McCoy singularities does not depend on the form of the disorder, provided the non-linear quantum control parameter has the same value. The exact scaling function of the magnetization with a small applied magnetic field is calculated and the critical point magnetization singularity is determined in a simple, direct way.Comment: 11 page

Nonequilibrium phase transition in a driven Potts model with friction

We consider magnetic friction between two systems of $q$-state Potts spins which are moving along their boundaries with a relative constant velocity $v$. Due to the interaction between the surface spins there is a permanent energy flow and the system is in a steady state which is far from equilibrium. The problem is treated analytically in the limit $v=\infty$ (in one dimension, as well as in two dimensions for large-$q$ values) and for $v$ and $q$ finite by Monte Carlo simulations in two dimensions. Exotic nonequilibrium phase transitions take place, the properties of which depend on the type of phase transition in equilibrium. When this latter transition is of first order, a sequence of second- and first-order nonequilibrium transitions can be observed when the interaction is varied.Comment: 13 pages, 9 figures, one journal reference adde

Droplets in the coexistence region of the two-dimensional Ising model

The two-dimensional Ising model with fixed magnetization is studied using Monte Carlo techniques. At the coexistence line, the macroscopic, extensive droplet of minority spins becomes thermally unstable by breaking up into microscopic clusters. Intriguing finite--size effects as well as singularities of thermal and cluster properties associated with the transition are discussed.Comment: 7 pages, 3 figures included, submitted to J. Phys. A: Math. Ge

An extreme ultraviolet spectrometer experiment for the Shuttle Get Away Special Program

An extreme ultraviolet (EUV) spectrometer experiment operated successfully during the STS-7 mission in an experiment to measure the global and diurnal variation of the EUV airglow. The spectrometer is an F 3.5 Wadsworth mount with mechanical collimator, a 75 x 75 mm grating, and a bare microchannel plate detector providing a spectral resolution of 7 X FWHM. Read-out of the signal is through discrete channels or resistive anode techniques. The experiment includes a microcomputer, 20 Mbit tape recorder, and a 28V, 40 Ahr silver-zinc battery. It is the first GAS payload to use an opening door. The spectrometer's 0.1 x 4.2 deg field of view is pointed vertically out of the shuttle bay. During the STS-7 flight data were acquired continuously for a period of 5 hours and 37 minutes, providing spectra of the 570 A to 850 A wavelength region of the airglow. Five diurnal cycles of the 584 A emission of neutral helium and the 834 A emission of ionized atomic oxygen were recorded. The experiment also recorded ion events and pressure pulses associated with thruster firings. The experiment is to fly again on Mission 41-F

Griffiths-McCoy singularities in random quantum spin chains: Exact results through renormalization

The Ma-Dasgupta-Hu renormalization group (RG) scheme is used to study singular quantities in the Griffiths phase of random quantum spin chains. For the random transverse-field Ising spin chain we have extended Fisher's analytical solution to the off-critical region and calculated the dynamical exponent exactly. Concerning other random chains we argue by scaling considerations that the RG method generally becomes asymptotically exact for large times, both at the critical point and in the whole Griffiths phase. This statement is checked via numerical calculations on the random Heisenberg and quantum Potts models by the density matrix renormalization group method.Comment: 4 pages RevTeX, 2 figures include

Zero--Temperature Quantum Phase Transition of a Two--Dimensional Ising Spin--Glass

We study the quantum transition at $T=0$ in the spin-$\frac12$ Ising spin--glass in a transverse field in two dimensions. The world line path integral representation of this model corresponds to an effective classical system in (2+1) dimensions, which we study by Monte Carlo simulations. Values of the critical exponents are estimated by a finite-size scaling analysis. We find that the dynamical exponent, $z$, and the correlation length exponent, $\nu$, are given by $z = 1.5 \pm 0.05$ and $\nu = 1.0 \pm 0.1$. Both the linear and non-linear susceptibility are found to diverge at the critical point.Comment: RevTeX 10 pages + 4 figures (appended as uuencoded, compressed tar-file), THP21-9

On the occurrence of oscillatory modulations in the power-law behavior of dynamic and kinetic processes in fractals

The dynamic and kinetic behavior of processes occurring in fractals with spatial discrete scale invariance (DSI) is considered. Spatial DSI implies the existence of a fundamental scaling ratio (b_1). We address time-dependent physical processes, which as a consequence of the time evolution develop a characteristic length of the form $\xi \propto t^{1/z}$, where z is the dynamic exponent. So, we conjecture that the interplay between the physical process and the symmetry properties of the fractal leads to the occurrence of time DSI evidenced by soft log-periodic modulations of physical observables, with a fundamental time scaling ratio given by $\tau = b_1 ^z$. The conjecture is tested numerically for random walks, and representative systems of broad universality classes in the fields of irreversible and equilibrium critical phenomena.Comment: 6 pages, 3 figures. Submitted to EP