7,975 research outputs found
New conjecture for the Perk-Schultz models
We present a new conjecture for the Perk-Schultz models. This
conjecture extends a conjecture presented in our article (Alcaraz FC and
Stroganov YuG (2002) J. Phys. A vol. 35 pg. 6767-6787, and also in
cond-mat/0204074).Comment: 3 pages 0 figure
Generalization of the matrix product ansatz for integrable chains
We present a general formulation of the matrix product ansatz for exactly
integrable chains on periodic lattices. This new formulation extends the matrix
product ansatz present on our previous articles (F. C. Alcaraz and M. J. Lazo
J. Phys. A: Math. Gen. 37 (2004) L1-L7 and J. Phys. A: Math. Gen. 37 (2004)
4149-4182.)Comment: 5 pages. to appear in J. Phys. A: Math. Ge
Exactly solvable interacting vertex models
We introduce and solvev a special family of integrable interacting vertex
models that generalizes the well known six-vertex model. In addition to the
usual nearest-neighbor interactions among the vertices, there exist extra
hard-core interactions among pair of vertices at larger distances.The
associated row-to-row transfer matrices are diagonalized by using the recently
introduced matrix product {\it ansatz}. Similarly as the relation of the
six-vertex model with the XXZ quantum chain, the row-to-row transfer matrices
of these new models are also the generating functions of an infinite set of
commuting conserved charges. Among these charges we identify the integrable
generalization of the XXZ chain that contains hard-core exclusion interactions
among the spins. These quantum chains already appeared in the literature. The
present paper explains their integrability.Comment: 20 pages, 3 figure
Nonlocal growth processes and conformal invariance
Up to now the raise and peel model was the single known example of a
one-dimensional stochastic process where one can observe conformal invariance.
The model has one-parameter.
Depending on its value one has a gapped phase, a critical point where one has
conformal invariance and a gapless phase with changing values of the dynamical
critical exponent . In this model, adsorption is local but desorption is
not. The raise and strip model presented here in which desorption is also
nonlocal, has the same phase diagram. The critical exponents are different as
are some physical properties of the model. Our study suggest the possible
existence of a whole class of stochastic models in which one can observe
conformal invariance.Comment: 27 pages, 22 figure
A conformal invariant growth model
We present a one-parameter extension of the raise and peel one-dimensional
growth model. The model is defined in the configuration space of Dyck (RSOS)
paths. Tiles from a rarefied gas hit the interface and change its shape. The
adsorption rates are local but the desorption rates are non-local, they depend
not only on the cluster hit by the tile but also on the total number of peaks
(local maxima) belonging to all the clusters of the configuration. The domain
of the parameter is determined by the condition that the rates are
non-negative. In the finite-size scaling limit, the model is conformal
invariant in the whole open domain. The parameter appears in the sound velocity
only. At the boundary of the domain, the stationary state is an adsorbing state
and conformal invariance is lost. The model allows to check the universality of
nonlocal observables in the raise and peel model. An example is given.Comment: 11 pages and 8 figure
Exact Solution of the Asymmetric Exclusion Model with Particles of Arbitrary Size
A generalization of the simple exclusion asymmetric model is introduced. In
this model an arbitrary mixture of molecules with distinct sizes , in units of lattice space, diffuses asymmetrically on the lattice.
A related surface growth model is also presented. Variations of the
distribution of molecules's sizes may change the excluded volume almost
continuously. We solve the model exactly through the Bethe ansatz and the
dynamical critical exponent is calculated from the finite-size corrections
of the mass gap of the related quantum chain. Our results show that for an
arbitrary distribution of molecules the dynamical critical behavior is on the
Kardar-Parizi-Zhang (KPZ) universality.Comment: 28 pages, 2 figures. To appear in Phys. Rev. E (1999
The Exact Solution of the Asymmetric Exclusion Problem With Particles of Arbitrary Size: Matrix Product Ansatz
The exact solution of the asymmetric exclusion problem and several of its
generalizations is obtained by a matrix product {\it ansatz}. Due to the
similarity of the master equation and the Schr\"odinger equation at imaginary
times the solution of these problems reduces to the diagonalization of a one
dimensional quantum Hamiltonian. We present initially the solution of the
problem when an arbitrary mixture of molecules, each of then having an
arbitrary size () in units of lattice spacing, diffuses
asymmetrically on the lattice. The solution of the more general problem where
we have | the diffusion of particles belonging to distinct class of
particles (), with hierarchical order, and arbitrary sizes is also
solved. Our matrix product {\it ansatz} asserts that the amplitudes of an
arbitrary eigenfunction of the associated quantum Hamiltonian can be expressed
by a product of matrices. The algebraic properties of the matrices defining the
{\it ansatz} depend on the particular associated Hamiltonian. The absence of
contradictions in the algebraic relations defining the algebra ensures the
exact integrability of the model. In the case of particles distributed in
classes, the associativity of the above algebra implies the Yang-Baxter
relations of the exact integrable model.Comment: 42 pages, 1 figur
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