13,269 research outputs found
A direct proof of Kim's identities
As a by-product of a finite-size Bethe Ansatz calculation in statistical
mechanics, Doochul Kim has established, by an indirect route, three
mathematical identities rather similar to the conjugate modulus relations
satisfied by the elliptic theta constants. However, they contain factors like
and , instead of . We show here that
there is a fourth relation that naturally completes the set, in much the same
way that there are four relations for the four elliptic theta functions. We
derive all of them directly by proving and using a specialization of
Weierstrass' factorization theorem in complex variable theory.Comment: Latex, 6 pages, accepted by J. Physics
Quantum Scaling Approach to Nonequilibrium Models
Stochastic nonequilibrium exclusion models are treated using a real space
scaling approach. The method exploits the mapping between nonequilibrium and
quantum systems, and it is developed to accommodate conservation laws and
duality symmetries, yielding exact fixed points for a variety of exclusion
models. In addition, it is shown how the asymmetric simple exclusion process in
one dimension can be written in terms of a classical Hamiltonian in two
dimensions using a Suzuki-Trotter decomposition.Comment: 17 page
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
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
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
Surface Critical Phenomena in Interaction-Round-a-Face Models
A general scheme has been proposed to study the critical behaviour of
integrable interaction-round-a-face models with fixed boundary conditions. It
has been shown that the boundary crossing symmetry plays an important role in
determining the surface free energy. The surface specific heat exponent can
thus be obtained without explicitly solving the reflection equations for the
boundary face weights. For the restricted SOS -state models of Andrews,
Baxter and Forrester the surface specific heat exponent is found to be
.Comment: 11 pages; Latex fil
Tricritical point of J1-J2 Ising model on hyperbolic lattice
A ferromagnetic-paramagnetic phase transition of the two-dimensional
frustrated Ising model on a hyperbolic lattice is investigated by use of the
corner transfer matrix renormalization group method. The model contains
ferromagnetic nearest-neighbor interaction J_1 and the competing
antiferromagnetic interaction J_2. A mean-field like second-order phase
transition is observed when the ratio \kappa = J_2 / J_1 is less than 0.203. In
the region 0.203 < \kappa < 1/4, the spontaneous magnetization is discontinuous
at the transition temperature. Such tricritical behavior suggests that the
phase transitions on hyperbolic lattices need not always be mean-field like.Comment: 7 pages, 13 figures, submitted to Phys. Rev.
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
Neogene paleoceanography of the eastern equatorial Pacific based on the radiolarian record of IODP drill sites off Costa Rica
The Integrated Ocean Drilling Program (IODP) Expedition 344 drilled cores following a transect across the convergent margin off Costa Rica. Two of the five sites (U1381 and U1414) are the subject of the present study. Major radiolarian faunal breaks and characteristic species groups were defined with the aid of cluster analysis, nodal analysis, and discriminant analysis of principal components. A middle-late Miocene to Pleistocene age (radiolarian zones RN5 to RN16) was determined for the sites, which agrees with the nannofossil zonations and 40Ar/39Ar and tephra layers. Considering the northward movement of the Cocos plate (∼7.3 cm/yr), and a paleolatitude calculator, it is assumed that during the Miocene the two sites were located ∼1000 km to the southwest of their current position, slightly south of the equator. The radiolarian faunas retrieved were thus seemingly formed under the influence of different oceanic currents and sources of nutrients. Changes in the radiolarian assemblages at Site U1414 point at dissimilar environmental settings associated with the colder South Equatorial Current and the warmer Equatorial Countercurrent, as well as to coastal upwelling. These differences are best reflected by changes in the abundance of the morphotype Spongurus spp., with noticeably higher values during the Miocene, than in the Pliocene and the Pleistocene. Because Spongurus spp. is generally associated with cooler waters, these abundance variations (as well as those of several other species) suggest that during the Miocene the area had a stronger influence of colder waters than during younger periods. During the Pliocene and the lowermost Pleistocene, biogenic remains are scarce, presumably due to the terrigenous input, which could have diluted and affected the preservation of pelagic fossils, as well as to the displacement of the site to warmer waters. A typically tropical fauna characterized the Pleistocene, yet with widespread presence of colder water species, most probably indicative of the influence of coastal upwelling processes.Fil: Sandoval, MarÃa I.. Universidad de Costa Rica; Costa Rica. Universite de Lausanne; SuizaFil: Boltovskoy, Demetrio. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de EcologÃa, Genética y Evolución de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de EcologÃa, Genética y Evolución de Buenos Aires; ArgentinaFil: Baxter, Alan T.. University of New England; Australia. McGill University; CanadáFil: Baumgartner, Peter O.. Universite de Lausanne; Suiz
Analyticity and Integrabiity in the Chiral Potts Model
We study the perturbation theory for the general non-integrable chiral Potts
model depending on two chiral angles and a strength parameter and show how the
analyticity of the ground state energy and correlation functions dramatically
increases when the angles and the strength parameter satisfy the integrability
condition. We further specialize to the superintegrable case and verify that a
sum rule is obeyed.Comment: 31 pages in harvmac including 9 tables, several misprints eliminate
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