230 research outputs found
On the S-matrix of the Sub-leading Magnetic Deformation of the Tricritical Ising Model in Two Dimensions
We compute the -matrix of the Tricritical Ising Model perturbed by the
subleading magnetic operator using Smirnov's RSOS reduction of the
Izergin-Korepin model. The massive model contains kink excitations which
interpolate between two degenerate asymmetric vacua. As a consequence of the
different structure of the two vacua, the crossing symmetry is implemented in a
non-trivial way. We use finite-size techniques to compare our results with the
numerical data obtained by the Truncated Conformal Space Approach and find good
agreement.Comment: 21 page
Algebraic arctic curves in the domain-wall six-vertex model
The arctic curve, i.e. the spatial curve separating ordered (or `frozen') and
disordered (or `temperate) regions, of the six-vertex model with domain wall
boundary conditions is discussed for the root-of-unity vertex weights. In these
cases the curve is described by algebraic equations which can be worked out
explicitly from the parametric solution for this curve. Some interesting
examples are discussed in detail. The upper bound on the maximal degree of the
equation in a generic root-of-unity case is obtained.Comment: 15 pages, no figures; v2: metadata correcte
On the problem of calculation of correlation functions in the six-vertex model with domain wall boundary conditions
The problem of calculation of correlation functions in the six-vertex model
with domain wall boundary conditions is addressed by considering a particular
nonlocal correlation function, called row configuration probability. This
correlation function can be used as building block for computing various (both
local and nonlocal) correlation functions in the model. The row configuration
probability is calculated using the quantum inverse scattering method; the
final result is given in terms of a multiple integral. The connection with the
emptiness formation probability, another nonlocal correlation function which
was computed elsewhere using similar methods, is also discussed.Comment: 15 pages, 2 figure
On the refined 3-enumeration of alternating sign matrices
AbstractAn explicit expression for the numbers A(n,r;3) describing the refined 3-enumeration of alternating sign matrices is given. The derivation is based on the recent results of Stroganov for the corresponding generating function. As a result, A(n,r;3)'s are represented as 1-fold sums which can also be written in terms of terminating F34 series of argument 1/4
Exact solution of Riemann--Hilbert problem for a correlation function of the XY spin chain
A correlation function of the XY spin chain is studied at zero temperature.
This is called the Emptiness Formation Probability (EFP) and is expressed by
the Fredholm determinant in the thermodynamic limit. We formulate the
associated Riemann--Hilbert problem and solve it exactly. The EFP is shown to
decay in Gaussian.Comment: 7 pages, to be published in J. Phys. Soc. Jp
The arctic curve of the domain-wall six-vertex model in its anti-ferroelectric regime
An explicit expression for the spatial curve separating the region of
ferroelectric order (`frozen' zone) from the disordered one (`temperate' zone)
in the six-vertex model with domain wall boundary conditions in its
anti-ferroelectric regime is obtained.Comment: 12 pages, 1 figur
The arctic curve of the domain-wall six-vertex model
The problem of the form of the `arctic' curve of the six-vertex model with
domain wall boundary conditions in its disordered regime is addressed. It is
well-known that in the scaling limit the model exhibits phase-separation, with
regions of order and disorder sharply separated by a smooth curve, called the
arctic curve. To find this curve, we study a multiple integral representation
for the emptiness formation probability, a correlation function devised to
detect spatial transition from order to disorder. We conjecture that the arctic
curve, for arbitrary choice of the vertex weights, can be characterized by the
condition of condensation of almost all roots of the corresponding saddle-point
equations at the same, known, value. In explicit calculations we restrict to
the disordered regime for which we have been able to compute the scaling limit
of certain generating function entering the saddle-point equations. The arctic
curve is obtained in parametric form and appears to be a non-algebraic curve in
general; it turns into an algebraic one in the so-called root-of-unity cases.
The arctic curve is also discussed in application to the limit shape of
-enumerated (with ) large alternating sign matrices. In
particular, as the limit shape tends to a nontrivial limiting curve,
given by a relatively simple equation.Comment: 39 pages, 2 figures; minor correction
Functional relations for the six vertex model with domain wall boundary conditions
In this work we demonstrate that the Yang-Baxter algebra can also be employed
in order to derive a functional relation for the partition function of the six
vertex model with domain wall boundary conditions. The homogeneous limit is
studied for small lattices and the properties determining the partition
function are also discussed.Comment: 19 pages, v2: typos corrected, new section and appendix added. v3:
minor corrections, to appear in J. Stat. Mech
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