8,519 research outputs found
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
Exact Solution of Asymmetric Diffusion With N Classes of Particles of Arbitrary Size and Hierarchical Order
The exact solution of the asymmetric exclusion problem with N distinct
classes of particles (c = 1,2,...,N), with hierarchical order is presented.
In this model the particles (size 1) are located at lattice points, and
diffuse with equal asymmetric rates, but particles in a class c do not
distinguish those in the classes c' >c from holes (empty sites). We generalize
and solve exactly this model by considering the molecules in each distinct
class c =1,2,...,N with sizes s_c (s_c = 0,1,2,...), in units of lattice
spacing. The solution is derived by a Bethe ansatz of nested type.Comment: 27 pages, 1 figur
Exact soultion of asymmetric diffusion with second-class particles of arbitrary size
The exact solution of the asymmetric exclusion problem with particles of
first and second class is presented. In this model the particles (size 1) of
both classes are attached on lattice points and diffuse with equal asymmetric
rates, but particles in the first class do not distinguish those in the second
class from the holes (empty sites). We generalize and solve exactly this model
by considering molecules in the first and second class with sizes and
(), in units of lattice spacing, respectively. The
solution is derived by a Bethe ansatz of nested type. We give in this paper a
pedagogical and simple presentation of the Bethe ansatz solution of the problem
which can easily be followed by a non specialized audience in exactly
integrable models.Comment: 21 pages, 7 figure
Exactly Solvable Interacting Spin-Ice Vertex Model
A special family of solvable five-vertex model is introduced on a square
lattice. In addition to the usual nearest neighbor interactions, the vertices
defining the model also interact alongone of the diagonals of the lattice. Such
family of models includes in a special limit the standard six-vertex model. The
exact solution of these models gives the first application of the matrix
product ansatz introduced recently and applied successfully in the solution of
quantum chains. The phase diagram and the free energy of the models are
calculated in the thermodynamic limit. The models exhibit massless phases and
our analyticaland numerical analysis indicate that such phases are governed by
a conformal field theory with central charge and continuosly varying
critical exponents.Comment: 14 pages, 11 figure
The pair annihilation reaction D + D --> 0 in disordered media and conformal invariance
The raise and peel model describes the stochastic model of a fluctuating
interface separating a substrate covered with clusters of matter of different
sizes, and a rarefied gas of tiles. The stationary state is obtained when
adsorption compensates the desorption of tiles. This model is generalized to an
interface with defects (D). The defects are either adjacent or separated by a
cluster. If a tile hits the end of a cluster with a defect nearby, the defect
hops at the other end of the cluster changing its shape. If a tile hits two
adjacent defects, the defect annihilate and are replaced by a small cluster.
There are no defects in the stationary state.
This model can be seen as describing the reaction D + D -->0, in which the
particles (defects) D hop at long distances changing the medium and annihilate.
Between the hops the medium also changes (tiles hit clusters changing their
shapes). Several properties of this model are presented and some exact results
are obtained using the connection of our model with a conformal invariant
quantum chain.Comment: 8 pages, 12figure
Asymmetric exclusion model with several kinds of impurities
We formulate a new integrable asymmetric exclusion process with
kinds of impurities and with hierarchically ordered dynamics.
The model we proposed displays the full spectrum of the simple asymmetric
exclusion model plus new levels. The first excited state belongs to these new
levels and displays unusual scaling exponents. We conjecture that, while the
simple asymmetric exclusion process without impurities belongs to the KPZ
universality class with dynamical exponent 3/2, our model has a scaling
exponent . In order to check the conjecture, we solve numerically the
Bethe equation with N=3 and N=4 for the totally asymmetric diffusion and found
the dynamical exponents 7/2 and 9/2 in these cases.Comment: to appear in JSTA
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
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