3,159 research outputs found
Determinant of the Potts model transfer matrix and the critical point
By using a decomposition of the transfer matrix of the -state Potts Model
on a three dimensional simple cubic lattice its
determinant is calculated exactly. By using the calculated determinants a
formula is conjectured which approximates the critical temperature for a
d-dimensional hypercubic lattice.Comment: 8 page
Quantum Group Representations and Baxter Equation
In this paper we propose algebraic universal procedure for deriving "fusion
rules" and Baxter equation for any integrable model with
symmetry of Quantum Inverse Scattering Method. Universal Baxter Q- operator is
got from the certain infinite dimensional representation called q-oscillator
one of the Universal R- matrix for affine algebra (first
proposed by V. Bazhanov, S.Lukyanov and A.Zamolodchikov for quantum KdV case).
We also examine the algebraic properties of Q-operator.Comment: 14 pages, Latex file, corrected references and acknowledgment
The triangular Ising model with nearest- and next-nearest-neighbor couplings in a field
We study the Ising model on the triangular lattice with nearest-neighbor
couplings , next-nearest-neighbor couplings , and a
magnetic field . This work is done by means of finite-size scaling of
numerical results of transfer matrix calculations, and Monte Carlo simulations.
We determine the phase diagram and confirm the character of the critical
manifolds. The emphasis of this work is on the antiferromagnetic case , but we also explore the ferromagnetic regime for H=0.
For and H=0 we locate a critical phase presumably covering the
whole range . For , we locate a
plane of phase transitions containing a line of tricritical three-state Potts
transitions. In the limit this line leads to a tricritical model
of hard hexagons with an attractive next-nearest-neighbor potential
Exact expectation values of local fields in quantum sine-Gordon model
We propose an explicit expression for vacuum expectation values of the
exponential fields in the sine-Gordon model. Our expression agrees both with
semi-classical results in the sine-Gordon theory and with perturbative
calculations in the Massive Thirring model. We use this expression to make new
predictions about the large-distance asymptotic form of the two-point
correlation function in the XXZ spin chain.Comment: 18 pages, harvmac.tex, 2 figure
The elliptic gamma function and SL(3,Z) x Z^3
The elliptic gamma function is a generalization of the Euler gamma function
and is associated to an elliptic curve. Its trigonometric and rational
degenerations are the Jackson q-gamma function and the Euler gamma function,
respectively. The elliptic gamma function appears in Baxter's formula for the
free energy of the eight-vertex model and in the hypergeometric solutions of
the elliptic qKZB equations. In this paper, the properties of this function are
studied. In particular we show that elliptic gamma functions are
generalizations of automorphic forms of G=SL(3,Z) x Z^3 associated to a
non-trivial class in H^3(G,Z).Comment: 27 pages, LaTeX References added, minor correction
Algebraic Bethe ansatz for the elliptic quantum group
To each representation of the elliptic quantum group is
associated a family of commuting transfer matrices. We give common eigenvectors
by a version of the algebraic Bethe ansatz method. Special cases of this
construction give eigenvectors for IRF models, for the eight-vertex model and
for the two-body Ruijsenaars operator. The latter is a -deformation of
Hermite's solution of the Lam\'e equation.Comment: 18 pages, AMSLaTe
Integrable Quantum Field Theories in Finite Volume: Excited State Energies
We develop a method of computing the excited state energies in Integrable
Quantum Field Theories (IQFT) in finite geometry, with spatial coordinate
compactified on a circle of circumference R. The IQFT ``commuting
transfer-matrices'' introduced by us (BLZ) for Conformal Field Theories (CFT)
are generalized to non-conformal IQFT obtained by perturbing CFT with the
operator . We study the models in which the fusion relations for
these ``transfer-matrices'' truncate and provide closed integral equations
which generalize the equations of Thermodynamic Bethe Ansatz to excited states.
The explicit calculations are done for the first excited state in the ``Scaling
Lee-Yang Model''.Comment: 54 pages, harvmac, epsf, TeX file and postscript figures packed in a
single selfextracting uufile. Compiles only in the `Big' mode with harvma
Yang-Baxter maps and symmetries of integrable equations on quad-graphs
A connection between the Yang-Baxter relation for maps and the
multi-dimensional consistency property of integrable equations on quad-graphs
is investigated. The approach is based on the symmetry analysis of the
corresponding equations. It is shown that the Yang-Baxter variables can be
chosen as invariants of the multi-parameter symmetry groups of the equations.
We use the classification results by Adler, Bobenko and Suris to demonstrate
this method. Some new examples of Yang-Baxter maps are derived in this way from
multi-field integrable equations.Comment: 20 pages, 5 figure
Dynamics of the 2d Potts model phase transition
The dynamics of 2d Potts models, which are temperature driven through the
phase transition using updating procedures in the Glauber universality class,
is investigated. We present calculations of the hysteresis for the (internal)
energy and for Fortuin-Kasteleyn clusters. The shape of the hysteresis is used
to define finite volume estimators of physical observables, which can be used
to study the approach to the infinite volume limit. We compare with equilibrium
configurations and the preliminary indications are that the dynamics leads to
considerable alterations of the statistical properties of the configurations
studied.Comment: Lattice2002(spin
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