8,630 research outputs found
The 1999 Heineman Prize Address- Integrable models in statistical mechanics: The hidden field with unsolved problems
In the past 30 years there have been extensive discoveries in the theory of
integrable statistical mechanical models including the discovery of non-linear
differential equations for Ising model correlation functions, the theory of
random impurities, level crossing transitions in the chiral Potts model and the
use of Rogers-Ramanujan identities to generalize our concepts of Bose/Fermi
statistics. Each of these advances has led to the further discovery of major
unsolved problems of great mathematical and physical interest. I will here
discuss the mathematical advances, the physical insights and extraordinary lack
of visibility of this field of physics.Comment: Text of the 1999 Heineman Prize address given March 24 at the
Centenial Meeting of the American Physical Society in Atlanta 20 pages in
latex, references added and typos correcte
Bailey flows and Bose-Fermi identities for the conformal coset models
We use the recently established higher-level Bailey lemma and Bose-Fermi
polynomial identities for the minimal models to demonstrate the
existence of a Bailey flow from to the coset models
where is a
positive integer and is fractional, and to obtain Bose-Fermi identities
for these models. The fermionic side of these identities is expressed in terms
of the fractional-level Cartan matrix introduced in the study of .
Relations between Bailey and renormalization group flow are discussed.Comment: 28 pages, AMS-Latex, two references adde
Randomly incomplete spectra and intermediate statistics
By randomly removing a fraction of levels from a given spectrum a model is
constructed that describes a crossover from this spectrum to a Poisson
spectrum. The formalism is applied to the transitions towards Poisson from
random matrix theory (RMT) spectra and picket fence spectra. It is shown that
the Fredholm determinant formalism of RMT extends naturally to describe
incomplete RMT spectra.Comment: 9 pages, 2 figures. To appear in Physical Review
Finite Temperature and Dynamical Properties of the Random Transverse-Field Ising Spin Chain
We study numerically the paramagnetic phase of the spin-1/2 random
transverse-field Ising chain, using a mapping to non-interacting fermions. We
extend our earlier work, Phys. Rev. 53, 8486 (1996), to finite temperatures and
to dynamical properties. Our results are consistent with the idea that there
are ``Griffiths-McCoy'' singularities in the paramagnetic phase described by a
continuously varying exponent , where measures the
deviation from criticality. There are some discrepancies between the values of
obtained from different quantities, but this may be due to
corrections to scaling. The average on-site time dependent correlation function
decays with a power law in the paramagnetic phase, namely
, where is imaginary time. However, the typical
value decays with a stretched exponential behavior, ,
where may be related to . We also obtain results for the full
probability distribution of time dependent correlation functions at different
points in the paramagnetic phase.Comment: 10 pages, 14 postscript files included. The discussion of the typical
time dependent correlation function has been greatly expanded. Other papers
of APY are available on-line at http://schubert.ucsc.edu/pete
Spin Chains as Perfect Quantum State Mirrors
Quantum information transfer is an important part of quantum information
processing. Several proposals for quantum information transfer along linear
arrays of nearest-neighbor coupled qubits or spins were made recently. Perfect
transfer was shown to exist in two models with specifically designed strongly
inhomogeneous couplings. We show that perfect transfer occurs in an entire
class of chains, including systems whose nearest-neighbor couplings vary only
weakly along the chain. The key to these observations is the Jordan-Wigner
mapping of spins to noninteracting lattice fermions which display perfectly
periodic dynamics if the single-particle energy spectrum is appropriate. After
a half-period of that dynamics any state is transformed into its mirror image
with respect to the center of the chain. The absence of fermion interactions
preserves these features at arbitrary temperature and allows for the transfer
of nontrivially entangled states of several spins or qubits.Comment: Abstract extended, introduction shortened, some clarifications in the
text, one new reference. Accepted by Phys. Rev. A (Rapid Communications
Boundary correlation function of fixed-to-free bcc operators in square-lattice Ising model
We calculate the boundary correlation function of fixed-to-free boundary
condition changing operators in the square-lattice Ising model. The correlation
function is expressed in four different ways using block Toeplitz
determinants. We show that these can be transformed into a scalar Toeplitz
determinant when the size of the matrix is even. To know the asymptotic
behavior of the correlation function at large distance we calculate the
asymptotic behavior of this scalar Toeplitz determinant using the Szeg\"o's
theorem and the Fisher-Hartwig theorem. At the critical temperature we confirm
the power-law behavior of the correlation function predicted by conformal field
theory
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