10,724 research outputs found
Multiple integral representation for the trigonometric SOS model with domain wall boundaries
Using the dynamical Yang-Baxter algebra we derive a functional equation for
the partition function of the trigonometric SOS model with domain wall boundary
conditions. The solution of the equation is given in terms of a multiple
contour integral.Comment: 28 pages, v2: comments and references added, typos fixed, to appear
in NP
Numerical Renormalization Group at Criticality
We apply a recently developed numerical renormalization group, the
corner-transfer-matrix renormalization group (CTMRG), to 2D classical lattice
models at their critical temperatures. It is shown that the combination of
CTMRG and the finite-size scaling analysis gives two independent critical
exponents.Comment: 5 pages, LaTeX, 5 figures available upon reques
Loop symmetry of integrable vertex models at roots of unity
It has been recently discovered in the context of the six vertex or XXZ model
in the fundamental representation that new symmetries arise when the anisotropy
parameter is evaluated at roots of unity . These new
symmetries have been linked to an invariance of the transfer
matrix and the corresponding spin-chain Hamiltonian.In this paper these results
are generalized for odd primitive roots of unity to all vertex models
associated with trigonometric solutions of the Yang-Baxter equation by invoking
representation independent methods which only take the algebraic structure of
the underlying quantum groups into account. Here is an
arbitrary Kac-Moody algebra. Employing the notion of the boost operator it is
then found that the Hamiltonian and the transfer matrix of the integrable model
are invariant under the action of . For the simplest case the discussion is also extended to even primitive roots of unity.Comment: tcilatex, 19 pages (minor typos corrected, one reference changed
The antiferromagnetic transition for the square-lattice Potts model
We solve the antiferromagnetic transition for the Q-state Potts model
(defined geometrically for Q generic) on the square lattice. The solution is
based on a detailed analysis of the Bethe ansatz equations (which involve
staggered source terms) and on extensive numerical diagonalization of transfer
matrices. It involves subtle distinctions between the loop/cluster version of
the model, and the associated RSOS and (twisted) vertex models. The latter's
continuum limit involves two bosons, one which is compact and twisted, and the
other which is not, with a total central charge c=2-6/t, for
sqrt(Q)=2cos(pi/t). The non-compact boson contributes a continuum component to
the spectrum of critical exponents. For Q generic, these properties are shared
by the Potts model. For Q a Beraha number [Q = 4 cos^2(pi/n) with n integer]
the two-boson theory is truncated and becomes essentially Z\_{n-2}
parafermions. Moreover, the vertex model, and, for Q generic, the Potts model,
exhibit a first-order critical point on the transition line, i.e., the critical
point is also the locus of level crossings where the derivatives of the free
energy are discontinuous. In that sense, the thermal exponent of the Potts
model is generically nu=1/2. Things are profoundly different for Q a Beraha
number, where the transition is second order, with nu=(t-2)/2 determined by the
psi\_1 parafermion. As one enters the adjacant Berker-Kadanoff phase, the model
flows, for t odd, to a minimal model of CFT with c=1-6/t(t-1), while for t even
it becomes massive. This provides a physical realization of a flow conjectured
by Fateev and Zamolodchikov in the context of Z\_N integrable perturbations.
Finally, we argue that the antiferromagnetic transition occurs as well on other
two-dimensional lattices
Auxiliary matrices for the six-vertex model and the algebraic Bethe ansatz
We connect two alternative concepts of solving integrable models, Baxter's
method of auxiliary matrices (or Q-operators) and the algebraic Bethe ansatz.
The main steps of the calculation are performed in a general setting and a
formula for the Bethe eigenvalues of the Q-operator is derived. A proof is
given for states which contain up to three Bethe roots. Further evidence is
provided by relating the findings to the six-vertex fusion hierarchy. For the
XXZ spin-chain we analyze the cases when the deformation parameter of the
underlying quantum group is evaluated both at and away from a root of unity.Comment: 32 page
Fateev-Zamolodchikov and Kashiwara-Miwa models: boundary star-triangle relations and surface critical properties
The boundary Boltzmann weights are found by solving the boundary
star-triangle relations for the Fateev-Zamolodchikov and Kashiwara-Miwa models.
We calculate the surface free energies of the models. The critical surface
exponent \alpha_s of the Kashiwara-Miwa model is given and satisfies the
scaling relation \alpha_b=2\alpha_s-2, where \alpha_b is the bulk exponent.Comment: 17 pages, no ps figures, latex fil
Heisenberg XYZ Hamiltonian with Integrable Impurities
In this letter, we construct a Hamiltonian of the impurity model within the
framework of the open boundary Heisenberg XYZ spin chain. This impurity model
is an exactly solved one and it degenerates to the integrable XXZ impurity
model under the triangular limit. This approach is the first time to add the
integrable impurities to the completely anisotropic Heisenberg spin model with
the open boundary conditions.Comment: 10 pages, LaTex (to appear in Physics Letters A
Bulk, surface and corner free energy series for the chromatic polynomial on the square and triangular lattices
We present an efficient algorithm for computing the partition function of the
q-colouring problem (chromatic polynomial) on regular two-dimensional lattice
strips. Our construction involves writing the transfer matrix as a product of
sparse matrices, each of dimension ~ 3^m, where m is the number of lattice
spacings across the strip. As a specific application, we obtain the large-q
series of the bulk, surface and corner free energies of the chromatic
polynomial. This extends the existing series for the square lattice by 32
terms, to order q^{-79}. On the triangular lattice, we verify Baxter's
analytical expression for the bulk free energy (to order q^{-40}), and we are
able to conjecture exact product formulae for the surface and corner free
energies.Comment: 17 pages. Version 2: added 4 further term to the serie
Relation of hyperlipidemia in serum and loss of high density lipoproteins in urine in the nephrotic syndrome
The mechanism leading to hyperlipidemia in the nephrotic syndrome is not fully understood but may be related in part to loss of high density lipoproteins in the urine of patients with nephrosis. To prove this hypothesis, we compared serum lipoprotein profiles with the excretion of high density lipoproteins in urine in 19 nephrotic patients. Serum cholesterol ranged from 19–152 (median value 45) mg/dl in very low density lipoproteins (VLDL), from 130–443 (median 186) mg/dl in low density lipoproteins (LDL) and from 19–64 (median 33) mg/dl in high density lipoproteins (HDL). Hyperlipoproteinemia was found in 17 patients, which was classified as phenotype IIa (Fredrickson) in 2, as phenotype IIb in 9 and as phenotype IV in 6 subjects. Two patients showed normal lipoprotein patterns. VLDL- and LDL-cholesterol were not found in detectable amounts in urine, whereas HDL-cholesterol was measured in low concentrations from 0.1–8.3 mg/24 h in all samples. There was no correlation between serum HDL-cholesterol and urinary HDL-cholesterol, but a positive correlation between serum LDL-cholesterol and urinary HDL-cholesterol (r= +0.54, p < 0.05). However, the total amount of the daily urinary loss of HDL (<1% of total plasma HDL) seems not to be sufficient to explain hyperlipoproteinemia in the nephrotic syndrome
- …