12,387 research outputs found
Exact low-temperature behavior of kagome antiferromagnet at high fields
Low-energy degrees of freedom of a spin-1/2 kagome antiferromagnet in the
vicinity of the saturation field are mapped to a hard-hexagon model on a
triangular lattice. The latter model is exactly solvable. The presented mapping
allows to obtain quantitative description of the magnetothermodynamics of a
quantum kagome antiferromagnet up to exponentially small corrections as well as
predict the critical behavior for the transition into a magnon crystal state.
Analogous mapping is presented for the sawtooth chain, which is mapped onto a
model of classical hard dimers on a chain.Comment: 5 pages, 2 figures, replaced with accepted versio
Bethe Ansatz Equations for the Broken -Symmetric Model
We obtain the Bethe Ansatz equations for the broken -symmetric
model by constructing a functional relation of the transfer matrix of
-operators. This model is an elliptic off-critical extension of the
Fateev-Zamolodchikov model. We calculate the free energy of this model on the
basis of the string hypothesis.Comment: 43 pages, latex, 11 figure
Exact solution and interfacial tension of the six-vertex model with anti-periodic boundary conditions
We consider the six-vertex model with anti-periodic boundary conditions
across a finite strip. The row-to-row transfer matrix is diagonalised by the
`commuting transfer matrices' method. {}From the exact solution we obtain an
independent derivation of the interfacial tension of the six-vertex model in
the anti-ferroelectric phase. The nature of the corresponding integrable
boundary condition on the spin chain is also discussed.Comment: 18 pages, LaTeX with 1 PostScript figur
Some comments on developments in exact solutions in statistical mechanics since 1944
Lars Onsager and Bruria Kaufman calculated the partition function of the
Ising model exactly in 1944 and 1949. Since then there have been many
developments in the exact solution of similar, but usually more complicated,
models. Here I shall mention a few, and show how some of the latest work seems
to be returning once again to the properties observed by Onsager and Kaufman.Comment: 28 pages, 5 figures, section on six-vertex model revise
Star-Triangle Relation for a Three Dimensional Model
The solvable -chiral Potts model can be interpreted as a
three-dimensional lattice model with local interactions. To within a minor
modification of the boundary conditions it is an Ising type model on the body
centered cubic lattice with two- and three-spin interactions. The corresponding
local Boltzmann weights obey a number of simple relations, including a
restricted star-triangle relation, which is a modified version of the
well-known star-triangle relation appearing in two-dimensional models. We show
that these relations lead to remarkable symmetry properties of the Boltzmann
weight function of an elementary cube of the lattice, related to spatial
symmetry group of the cubic lattice. These symmetry properties allow one to
prove the commutativity of the row-to-row transfer matrices, bypassing the
tetrahedron relation. The partition function per site for the infinite lattice
is calculated exactly.Comment: 20 pages, plain TeX, 3 figures, SMS-079-92/MRR-020-92. (corrupted
figures replaced
Lattice gas description of pyrochlore and checkerboard antiferromagnets in a strong magnetic field
Quantum Heisenberg antiferromagnets on pyrochlore and checkerboard lattices
in a strong external magnetic field are mapped onto hard-core lattice gases
with an extended exclusion region. The effective models are studied by the
exchange Monte Carlo simulations and by the transfer matrix method. The
transition point and the critical exponents are obtained numerically for a
square-lattice gas of particles with the second-neighbor exclusion, which
describes a checkerboard antiferromagnet. The exact structure of the magnon
crystal state is determined for a pyrochlore antiferromagnet.Comment: 11 pages, accepted versio
Phase-field approach to heterogeneous nucleation
We consider the problem of heterogeneous nucleation and growth. The system is
described by a phase field model in which the temperature is included through
thermal noise. We show that this phase field approach is suitable to describe
homogeneous as well as heterogeneous nucleation starting from several general
hypotheses. Thus we can investigate the influence of grain boundaries,
localized impurities, or any general kind of imperfections in a systematic way.
We also put forward the applicability of our model to study other physical
situations such as island formation, amorphous crystallization, or
recrystallization.Comment: 8 pages including 7 figures. Accepted for publication in Physical
Review
Construction of some missing eigenvectors of the XYZ spin chain at the discrete coupling constants and the exponentially large spectral degeneracy of the transfer matrix
We discuss an algebraic method for constructing eigenvectors of the transfer
matrix of the eight vertex model at the discrete coupling parameters. We
consider the algebraic Bethe ansatz of the elliptic quantum group for the case where the parameter satisfies for arbitrary integers , and . When or
is odd, the eigenvectors thus obtained have not been discussed previously.
Furthermore, we construct a family of degenerate eigenvectors of the XYZ spin
chain, some of which are shown to be related to the loop algebra
symmetry of the XXZ spin chain. We show that the dimension of some degenerate
eigenspace of the XYZ spin chain on sites is given by , if
is an even integer. The construction of eigenvectors of the transfer matrices
of some related IRF models is also discussed.Comment: 19 pages, no figure (revisd version with three appendices
Comment on `Equilibrium crystal shape of the Potts model at the first-order transition point'
We comment on the article by Fujimoto (1997 J. Phys. A: Math. Gen., Vol. 30,
3779), where the exact equilibrium crystal shape (ECS) in the critical Q-state
Potts model on the square lattice was calculated, and its equivalence with ECS
in the Ising model was established. We confirm these results, giving their
alternative derivation applying the transformation properties of the
one-particle dispersion relation in the six-vertex model. It is shown, that
this dispersion relation is identical with that in the Ising model on the
square lattice.Comment: 4 pages, 1 figure, LaTeX2
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