4,392 research outputs found
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 () as and is oscillatory or
non-oscillatory depending on the magnitude of the transverse field.Comment: 5 pages, 1 figur
Lunar particle shadows and boundary layer experiment: Plasma and energetic particles on the Apollo 15 and 16 subsatellites
The lunar particle shadows and boundary layer experiments aboard the Apollo 15 and 16 subsatellites and scientific reduction and analysis of the data to date are discussed with emphasis on four major topics: solar particles; interplanetry particle phenomena; lunar interactions; and topology and dynamics of the magnetosphere at lunar orbit. The studies of solar and interplanetary particles concentrated on the low energy region which was essentially unexplored, and the studies of lunar interaction pointed up the transition from single particle to plasma characteristics. The analysis concentrated on the electron angular distributions as highly sensitive indicators of localized magnetization of the lunar surface. Magnetosphere experiments provided the first electric field measurements in the distant magnetotail, as well as comprehensive low energy particle measurements at lunar distance
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 , 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 . 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
More than a cognitive experience: unfamiliarity, invalidation, and emotion in organizational learning
Literature on organizational learning (OL) lacks an integrative framework that captures the emotions involved as OL proceeds. Drawing on personal construct theory, we suggest that organizations learn where their members reconstrue meaning around questions of strategic significance for the organization. In this 5-year study of an electronics company, we explore the way in which emotions change as members perceive progress or a lack of progress around strategic themes. Our framework also takes into account whether OL involves experiences that are familiar or unfamiliar and the implications for emotions. We detected similar patterns of emotion arising over time for three different themes in our data, thereby adding to OL perspectives that are predominantly cognitive in orientation
Dimer and N\'eel order-parameter fluctuations in the spin-fluid phase of the s=1/2 spin chain with first and second neighbor couplings
The dynamical properties at T=0 of the one-dimensional (1D) s=1/2
nearest-neighbor (nn) XXZ model with an additional isotropic
next-nearest-neighbor (nnn) coupling are investigated by means of the recursion
method in combination with techniques of continued-fraction analysis. The focus
is on the dynamic structure factors S_{zz}(q,\omega) and S_{DD}(q,\omega),
which describe (for q=\pi) the fluctuations of the N\'eel and dimer order
parameters, respectively. We calculate (via weak-coupling continued-fraction
analysis) the dependence on the exchange constants of the infrared exponent,
the renormalized bandwidth of spinon excitations, and the spectral-weight
distribution in S_{zz}(\pi,\omega) and S_{DD}(\pi,\omega), all in the
spin-fluid phase, which is realized for planar anisotropy and sufficiently
weak nnn coupling. For some parameter values we find a discrete branch of
excitations above the spinon continuum. They contribute to S_{zz}(q,\omega) but
not to S_{DD}(q,\omega).Comment: RevTex file (7 pages), 8 figures (uuencoded ps file) available from
author
Lifespan theorem for constrained surface diffusion flows
We consider closed immersed hypersurfaces in and evolving by
a class of constrained surface diffusion flows. Our result, similar to earlier
results for the Willmore flow, gives both a positive lower bound on the time
for which a smooth solution exists, and a small upper bound on a power of the
total curvature during this time. By phrasing the theorem in terms of the
concentration of curvature in the initial surface, our result holds for very
general initial data and has applications to further development in asymptotic
analysis for these flows.Comment: 29 pages. arXiv admin note: substantial text overlap with
arXiv:1201.657
Monte Carlo study of the evaporation/condensation transition on different Ising lattices
In 2002 Biskup et al. [Europhys. Lett. 60, 21 (2002)] sketched a rigorous
proof for the behavior of the 2D Ising lattice gas, at a finite volume and a
fixed excess \delta M of particles (spins) above the ambient gas density
(spontaneous magnetisation). By identifying a dimensionless parameter \Delta
(\delta M) and a universal constant \Delta_c, they showed in the limit of large
system sizes that for \Delta < \Delta_c the excess is absorbed in the
background (``evaporated'' system), while for \Delta > \Delta_c a droplet of
the dense phase occurs (``condensed'' system).
To check the applicability of the analytical results to much smaller,
practically accessible system sizes, we performed several Monte Carlo
simulations for the 2D Ising model with nearest-neighbour couplings on a square
lattice at fixed magnetisation M. Thereby, we measured the largest minority
droplet, corresponding to the condensed phase, at various system sizes (L=40,
>..., 640). With analytic values for for the spontaneous magnetisation m_0, the
susceptibility \chi and the Wulff interfacial free energy density \tau_W for
the infinite system, we were able to determine \lambda numerically in very good
agreement with the theoretical prediction.
Furthermore, we did simulations for the spin-1/2 Ising model on a triangular
lattice and with next-nearest-neighbour couplings on a square lattice. Again,
finding a very good agreement with the analytic formula, we demonstrate the
universal aspects of the theory with respect to the underlying lattice. For the
case of the next-nearest-neighbour model, where \tau_W is unknown analytically,
we present different methods to obtain it numerically by fitting to the
distribution of the magnetisation density P(m).Comment: 14 pages, 17 figures, 1 tabl
Universal role of correlation entropy in critical phenomena
In statistical physics, if we successively divide an equilibrium system into
two parts, we will face a situation that, within a certain length , the
physics of a subsystem is no longer the same as the original system. Then the
extensive properties of the thermal entropy ABAB is
violated. This observation motivates us to introduce the concept of correlation
entropy between two points, as measured by mutual information in the
information theory, to study the critical phenomena. A rigorous relation is
established to display some drastic features of the non-vanishing correlation
entropy of the subsystem formed by any two distant particles with long-range
correlation. This relation actually indicates the universal role of the
correlation entropy in understanding critical phenomena. We also verify these
analytical studies in terms of two well-studied models for both the thermal and
quantum phase transitions: two-dimensional Ising model and one-dimensional
transverse field Ising model. Therefore, the correlation entropy provides us
with a new physical intuition in critical phenomena from the point of view of
the information theory.Comment: 10 pages, 9 figure
The open XXZ-chain: Bosonisation, Bethe ansatz and logarithmic corrections
We calculate the bulk and boundary parts of the free energy for an open
spin-1/2 XXZ-chain in the critical regime by bosonisation. We identify the
cutoff independent contributions and determine their amplitudes by comparing
with Bethe ansatz calculations at zero temperature T. For the bulk part of the
free energy we find agreement with Lukyanov's result [Nucl.Phys.B 522, 533
(1998)]. In the boundary part we obtain a cutoff independent term which is
linear in T and determines the temperature dependence of the boundary
susceptibility in the attractive regime for . We further show that at
particular anisotropies where contributions from irrelevant operators with
different scaling dimensions cross, logarithmic corrections appear. We give
explicit formulas for these terms at those anisotropies where they are most
important. We verify our results by comparing with extensive numerical
calculations based on a numerical solution of the T=0 Bethe ansatz equations,
the finite temperature Bethe ansatz equations in the quantum-transfer matrix
formalism, and the density-matrix renormalisation group applied to transfer
matrices.Comment: 35 pages, 8 figure
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,
, which is a natural measure of the distance from the quantum critical
point. , 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
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