5,761 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
Role of OH-stretch/torsion coupling and quantum yield effects in the first OH overtone spectrum of cis-cis HOONO
A joint theoretical and experimental investigation is undertaken to study the effects of OH-stretch/HOON torsion coupling and of quantum yield on the previously reported first overtone action spectrum of cis-cis HOONO (peroxynitrous acid). The minimum energy path along the HOON dihedral angle is computed at the coupled cluster singles and doubles with perturbative triples level with correlation consistent polarized quadruple zeta basis set, at the structure optimized using the triple zeta basis set (CCSD(T)/cc-pVQZ//CCSD(T)/cc-pVTZ). The two-dimensional ab initio potential energy and dipole moment surfaces for cis-cis HOONO are calculated as functions of the HOON torsion and OH bond length about the minimum energy path at the CCSD(T)/cc-pVTZ and QCISD/AUG-cc-pVTZ (QCISD—quadratic configuration interaction with single and double excitation and AUG-augmented with diffuse functions) level of theory/basis, respectively. The OH-stretch vibration depends strongly on the torsional angle, and the torsional potential possesses a broad shelf at ~90°, the cis-perp conformation. The calculated electronic energies and dipoles are fit to simple functional forms and absorption spectra in the region of the OH fundamental and first overtone are calculated from these surfaces. While the experimental and calculated spectra of the OH fundamental band are in good agreement, significant differences in the intensity patterns are observed between the calculated absorption spectrum and the measured action spectrum in the 2nuOH region. These differences are attributed to the fact that several of the experimentally accessible states do not have sufficient energy to dissociate to OH+NO2 and therefore are not detectable in an action spectrum. Scaling of the intensities of transitions to these states, assuming D0=82.0 kJ/mol, is shown to produce a spectrum that is in good agreement with the measured action spectrum. Based on this agreement, we assign two of the features in the spectrum to Delta n=0 transitions (where n is the HOON torsion quantum number) that are blue shifted relative to the origin band, while the large peak near 7000 cm^–1 is assigned to a series of Delta n=+1 transitions, with predominant contributions from torsionally excited states with substantial cis-perp character. The direct absorption spectrum of cis-cis HOONO (6300–6850 cm^–1) is recorded by cavity ringdown spectroscopy in a discharge flow cell. A single band of HOONO is observed at 6370 cm^–1 and is assigned as the origin of the first OH overtone of cis-cis HOONO. These results imply that the origin band is suppressed by over an order of magnitude in the action spectrum, due to a reduced quantum yield. The striking differences between absorption and action spectra are correctly predicted by the calculations
The Q-operator and Functional Relations of the Eight-vertex Model at Root-of-unity for odd N
Following Baxter's method of producing Q_{72}-operator, we construct the
Q-operator of the root-of-unity eight-vertex model for the crossing parameter
with odd where Q_{72} does not exist. We use this
new Q-operator to study the functional relations in the Fabricius-McCoy
comparison between the root-of-unity eight-vertex model and the superintegrable
N-state chiral Potts model. By the compatibility of the constructed Q-operator
with the structure of Baxter's eight-vertex (solid-on-solid) SOS model, we
verify the set of functional relations of the root-of-unity eight-vertex model
using the explicit form of the Q-operator and fusion weights of SOS model.Comment: Latex 28 page; Typos corrected, minor changes in presentation,
References added and updated-Journal versio
Ising Dynamics with Damping
We show for the Ising model that is possible construct a discrete time
stochastic model analogous to the Langevin equation that incorporates an
arbitrary amount of damping. It is shown to give the correct equilibrium
statistics and is then used to investigate nonequilibrium phenomena, in
particular, magnetic avalanches. The value of damping can greatly alter the
shape of hysteresis loops, and for small damping and high disorder, the
morphology of large avalanches can be drastically effected. Small damping also
alters the size distribution of avalanches at criticality.Comment: 8 pages, 8 figures, 2 colum
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
The Q-operator for Root-of-Unity Symmetry in Six Vertex Model
We construct the explicit -operator incorporated with the
-loop-algebra symmetry of the six-vertex model at roots of unity. The
functional relations involving the -operator, the six-vertex transfer matrix
and fusion matrices are derived from the Bethe equation, parallel to the
Onsager-algebra-symmetry discussion in the superintegrable -state chiral
Potts model. We show that the whole set of functional equations is valid for
the -operator. Direct calculations in certain cases are also given here for
clearer illustration about the nature of the -operator in the symmetry study
of root-of-unity six-vertex model from the functional-relation aspect.Comment: Latex 26 Pages; Typos and small errors corrected, Some explanations
added for clearer presentation, References updated-Journal version with
modified labelling of sections and formula
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
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
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
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