The exact phase diagram of the quantumXY spin glass model in a transverse field

The infinite rangeXY spin glass model in a transverse field is investigated by means of the Trotter-Suzuki approach. The exact phase diagram is obtained showing that a spin glass transition takes place for non-zero values of the transverse field up to a critical value _c =1.440.01. The present numerically exact calculations are in good agreement with our previous approximate results and they clear remaining discrepancies from previous work.     

High-frequency sum rules for the quasi-one-dimensional quantum plasma dielectric tensor. II. Spin effect

We derive a high-frequency expansion for all elements of the quasi-one-dimensional quantum plasma dielectric tensor atT=0 K for quantum particles with spins. In addition to the known results for spinless case, we find that _S.5 ^Emphasis>/12 (k) and _S.5 ²³ (k) are the only frequency moments of the dielectric tensor with spin terms. Further, we find that there is no spin effect on quantum plasma dispersion for both ordinary and transverse modes propagating either along or across the external field.     

Field theory of critical behavior in a driven diffusive system

We use a field theoretic renormalization group method to study the critical properties of a diffusive system with a single conserved density subject to a constant uniform external field. A fixed point stable belowd _c=5 is found to govern the critical behavior. Scaling forms of density correlation functions are derived and critical exponents are obtained to all orders in =5–d. Spatial correlations are found to be very anisotropic with elongated correlations along the external field. Long wavelength transverse fluctuations are suppressed completely to yield mean field transverse exponents.     

Convergence to the ground-state energy in the thermodynamic limit of the Ising model in a strong transverse field

For the quantum mechanical Ising model in a strong transverse field we show that the convergence of the ground-state energy per site as the volume goes to infinity has an Ornstein-Zernicke behavior. That is, if the diameter of thed-dimensional lattice is given byL, the absolute value of the difference of the ground-state energy per site and its limit is asymptotically exp(-L)L ^–d/2 for some positive constant. We also show that the correlation function has the same behavior. Our results are derived by cluster expansions, using a method of Bricmont and Fröhlich which we extend to the quantum mechanical case.     

Phase transitions in the Ising model with transverse field

We show the existence of a phase transition in the Ising model with transverse field for dimensionsv 2 provided the transverse term is sufficiently small. This is done by proving long-range order occurs using the reflection positivity of the Hamiltonian and localization of eigenvectors.     

Trapping aspects in enhanced diffusion

We study the superlinear diffusion x ²(t) t , > 1, in layered media containing random velocity fields. The superlinear behavior holds in the case of random velocities along thex direction accompanied by diffusional motion in the space transverse to it. The transverse space can be either Euclidean, fractal, or ultrametric. For a one-dimensional transverse space we derive exact expressions for the higher moments of the displacement. Furthermore, we investigate the propagatorP(x, t) along thex direction and establish its scaling behavior. Our analysis highlights the resemblance between the stretched-Gaussian behavior of the propagator and the stretched-exponential form of the survivial probability in the trapping problem; both show late crossover behavior.This work is dedicated to Prof. George H. Weiss.     

Transverse waves in a relativistic rigid body

We present relativistic elasticity as a scalar field theory. We apply it to rigid bodies, i.e., relativistic bodies with a nonlinear elastic law and a definite longitudinal wave velocity _l equal to the light velocity,c. We obtain the transverse wave equation with a definite velocity _t , and the relation between _l , _t , and the Poisson coefficient is the classical one. This is an indication that we have the relativistic extension of a classical Hooke elastic law.     

Low temperature nonequilibrium dynamics in transverse Ising spin glass

The real part of the time-dependent ac susceptibility of the short-range Ising spin glass in a transverse field has been investigated at very low temperatures. We have used the quantum linear response theory and domain coarsening ideas of quantum droplet scaling theory. It is found that after a temperature quench to a temperature T ₁ (lower than the spin glass transition temperature T _g ) the ac susceptibility decreases with time approximately in a logarithmic way as the system tends to the equilibrium. It is shown that the transverse field of tunneling has unessential effect on the nonequilibrium dynamical properties of the magnetic droplet system. The role of quantum fluctuations in the behavior of the ac susceptibility is discussed.Received: 26 February 2004, Published online: 18 June 2004PACS: 75.40.Gb Dynamic properties (dynamic susceptibility, spin waves, spin diffusion, dynamic scaling, etc.) - 75.10.Nr Spin-glass and other random models - 75.50.Lk Spin glasses and other random magnets     

Zero fieldμ + spin relaxation in some REAl2 intermetallics

Transverse field measurements on the rare-earths intermetallics REAl₂ in their paramagnetic regime have previously been carried out [1]. To aid discrimination between inhomogeneous line broadening and RE fluctuations which both contribute to the damping of the transverseSR pattern, we have carried out zero field measurements on three selected compounds (PrAl₂, GdAl₂, DyAl₂) between 300 and 25 K. A small longitudinal decoupling field (6 mT) was applied in some cases. The present data corroborate the findings of the transverse field study: The polarization rate increases rapidly when approaching magnetic order. The high temperature limit of the spin fluctuation rate is markedly different in the three compounds. The ⁺ diffuses rapidly in all REAl₂ compounds.     

Dynamics of Alternating Spin Chains

We consider the dimerised spin- isotropic XY chain in a transverse field and study the xx and zz dynamic structure factors for different values of the Hamiltonian parameters and temperature.     

Transverse hall-conductivity in the Landau-subbands of a 2D-lattice

Some numerical results concerning the variation of the transverse hall-conductivity _xy atT=0 within the Landau-subbands of a 2D-tight-binding model with a rational magnetic field are presented.Work supported in part by the Sonderforschungsbereich 123 Stochastic Mathematical Models of the Deutsche Forschungsgemeinschaft     

Full vector treatment of the polarization evolution in an arbitrary field distribution

This paper presents a vector representation of the ensemble muon polarizationP(t) for static field distributions which emphasizes the different behavior resulting from correlated and non-correlated field distributions. For example, with most local field distributions, such as random dipolar fields, the net muon polarization in the limit of infinite timeP(t) is parallel to the initial muon spin direction when the using transverse field (TF) or longitudinal field (LF) geometries. In general, however, it need not be; this will be demonstrated using the field distribution of an anisotropic superconductor.     

Mobility of muons in Cu below 2 K

We have performed transverse fieldSR experiments on several different samples of copper in the temperature range below 2 K, including isotope separated Cu and impurity doped polycrystalline Cu.We do not observe any strong effect of the isotope composition of the sample. A⁶³Cu and a natural Cu sample of identical purity both yield 0.16s^–1 for the low-temperature plateau, while an increased linewidth in the⁶⁵Cu case may be related to the strong effects of Fe impurities.Careful transverse field measurements on large single crystals at 0.08 K reveal non-Gaussian lineshapes in accordance with the picture of diffusing muons at this temperature. This allows us to reject several of the existing models for muon behaviour in copper below 2 K.     

Temperature dependence of the magnetic penetration depth in YBa2Cu3O6.95

We report precision transverse fieldSR measurements of the internal field distribution in the vortex state of crystalline YBa₂Cu₃O_6.95. A novel low background apparatus was used to study a mosaic sample of three high quality single crystals (T_c=93.3K). The observed frequency spectra in magnetic fields of 5kG and 15 kG applied along the c-axis have the characteristic features expected for a regular vortex lattice with some additional broadening. From a preliminary analysis we find that [(0)/(T)]² has a linear temperature coefficient forT<30 K. Such a term is inconsistent with simple s-wave pairing in the superconducting state. These results support recent microwave measurements of(T) on similar crystals in zero applied field but differ significantly from previousSR reports on sintered powders and crystals with lower T_c.This research was supported by the Natural Sciences and Engineering Research Council of Canada.     

Determination of λ and κ in a mosaic of single crystal YBa2Cu3O6.95

We present transverse fieldSR measurements of the magnetic field distribution in a mosaic of single crystal YBa₂Cu₃O_6.95 in high fields (1.9–6.5 T) applied parallel to the crystallographicc-axis. TheSR lineshapes are shown in detail and the results of fits to the lineshapes are summarized.     

Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. I. General Theory and Square-Lattice Chromatic Polynomial

We study the chromatic polynomials (= zero-temperature antiferromagnetic Potts-model partition functions) P _G (q) for m×n rectangular subsets of the square lattice, with m8 (free or periodic transverse boundary conditions) and n arbitrary (free longitudinal boundary conditions), using a transfer matrix in the Fortuin–Kasteleyn representation. In particular, we extract the limiting curves of partition-function zeros when n, which arise from the crossing in modulus of dominant eigenvalues (Beraha–Kahane–Weiss theorem). We also provide evidence that the Beraha numbers B ₂,B ₃,B ₄,B ₅ are limiting points of partition-function zeros as n whenever the strip width m is 7 (periodic transverse b.c.) or 8 (free transverse b.c.). Along the way, we prove that a noninteger Beraha number (except perhaps B ₁₀) cannot be a chromatic root of any graph.     

Space-Charge Field Induced in a Photorefractive Crystal with an Applied Square-Wave Electric Field for Large Contrast of an Interference Pattern

In the quasi-static approximation, the nonlinear equation for the space-charge field E _sc formed in a photorefractive crystal with an applied square-wave voltage under the action of light with an inhomogeneous transverse intensity distribution is derived. The spatial spectrum of the field E _sc induced in a Bi₁₂TiO₂₀ crystal with typical values of the acceptor density N _A and of the product of the electron mobility by the recombination time _R is analyzed. An approximate analytical solution of the nonlinear equation is derived in the case in which the amplitudes of spatial harmonics of the spectrum E _sc form a nonmonotonic sequence. The spatial distribution of the induced electric field is calculated numerically for crystals with different parameters N _A and _R .     

MHD laminar thin-film flow along a vertcal wall

An accelerating magnetohydrodynamic laminar flow of an electrically conducting fluid under the influence of gravity and in presence of transverse magnetic field is investigated in the paper. Using a cubic polynomial for the velocity profile inside the boundary layer, the momentum integral equation is solved numerically by Runge-Kutta method to determine the boundary layer thickness and the corresponding film thickness is then calculated for the entrance region. The effect of magnetic field on these solutions is shown in graphical form.List of symbols u, v local velocity components - p pressure - density - kinematic viscosity - viscosity= - electrical conductivity - g acceleration due to gravity - U _s (x) inviscid core velocity - h(x) film thicknes - (x) boundary layer thickness - M Hartmann number - B ₀ external magnetic field The authors remain thankful to the referee for some helpful criticisms.     

Search for photon regeneration in a magnetic field

We have searched for the regeneration of photons propagating in a transverse magnetic field. Such an effect would reveal the existence of light scalar or pseudoscalar particles such as the axion that couple to two photons. We obtain for this coupling the limitg _a<>⁶ GeV)^–1, provided the axion massm _a 10^–3 eV.     

Hydrodynamic theory of electron transport in a strong magnetic field

The mode coupling contribution to the transverse transport coefficients of a three-dimensional one-component plasma in a strong external magnetic field is calculated. For very strong fields it is found that the tagged particle diffusion rate, the thermal diffusion rate, and the coefficient of viscosity in the plane orthogonal to the field have a Bohm-like B ^–1 behavior. The mode coupling mechanism responsible for such an effect is always one that involves the finite-frequency upper hybrid modes.