5 research outputs found
Algebras in Higher Dimensional Statistical Mechanics - the Exceptional Partition (MEAN Field) Algebras
We determine the structure of the partition algebra (a generalized
Temperley-Lieb algebra) for specific values of Q \in \C, focusing on the
quotient which gives rise to the partition function of site -state Potts
models (in the continuous formulation) in arbitrarily high lattice
dimensions (the mean field case). The algebra is non-semi-simple iff is a
non-negative integer less than . We determine the dimension of the key
irreducible representation in every specialization.Comment: 4 page
Low temperature spin diffusion in the one-dimensional quantum nonlinear -model
An effective, low temperature, classical model for spin transport in the
one-dimensional, gapped, quantum non-linear -model is developed.
Its correlators are obtained by a mapping to a model solved earlier by Jepsen.
We obtain universal functions for the ballistic-to-diffusive crossover and the
value of the spin diffusion constant, and these are claimed to be exact at low
temperatures. Implications for experiments on one-dimensional insulators with a
spin gap are noted.Comment: 4 pages including 3 eps-figures, Revte
A note on graded Yang-Baxter solutions as braid-monoid invariants
We construct two solutions of the graded Yang-Baxter equation by
using the algebraic braid-monoid approach. The factorizable S-matrix
interpretation of these solutions is also discussed.Comment: 7 pages, UFSCARF-TH-94-1
Theory of Two-Dimensional Quantum Heisenberg Antiferromagnets with a Nearly Critical Ground State
We present the general theory of clean, two-dimensional, quantum Heisenberg
antiferromagnets which are close to the zero-temperature quantum transition
between ground states with and without long-range N\'{e}el order. For
N\'{e}el-ordered states, `nearly-critical' means that the ground state
spin-stiffness, , satisfies , where is the
nearest-neighbor exchange constant, while `nearly-critical' quantum-disordered
ground states have a energy-gap, , towards excitations with spin-1,
which satisfies . Under these circumstances, we show that the
wavevector/frequency-dependent uniform and staggered spin susceptibilities, and
the specific heat, are completely universal functions of just three
thermodynamic parameters. Explicit results for the universal scaling functions
are obtained by a expansion on the quantum non-linear sigma model,
and by Monte Carlo simulations. These calculations lead to a variety of
testable predictions for neutron scattering, NMR, and magnetization
measurements. Our results are in good agreement with a number of numerical
simulations and experiments on undoped and lightly-doped .Comment: 81 pages, REVTEX 3.0, smaller updated version, YCTP-xxx
Off-Shell Bethe Ansatz Equation and N-point Correlators in the SU(2) WZNW Theory
We prove that the wave vectors of the off-shell Bethe Ansatz equation for the
inhomogeneous SU(2) lattice vertex model render in the quasiclassical limit the
solution of the Knizhnik-Zamolodchikov equation.Comment: LaTeX, 15 page