10,241 research outputs found
The Complex of Solutions of the Nested Bethe Ansatz. The A_2 Spin Chain
The full set of polynomial solutions of the nested Bethe Ansatz is
constructed for the case of A_2 rational spin chain. The structure and
properties of these associated solutions are more various then in the case of
usual XXX (A_1) spin chain but their role is similar
Algorithms for entanglement renormalization
We describe an iterative method to optimize the multi-scale entanglement
renormalization ansatz (MERA) for the low-energy subspace of local Hamiltonians
on a D-dimensional lattice. For translation invariant systems the cost of this
optimization is logarithmic in the linear system size. Specialized algorithms
for the treatment of infinite systems are also described. Benchmark simulation
results are presented for a variety of 1D systems, namely Ising, Potts, XX and
Heisenberg models. The potential to compute expected values of local
observables, energy gaps and correlators is investigated.Comment: 23 pages, 28 figure
A Generalized Q-operator for U_q(\hat(sl_2)) Vertex Models
In this paper, we construct a Q-operator as a trace of a representation of
the universal R-matrix of over an infinite-dimensional
auxiliary space. This auxiliary space is a four-parameter generalization of the
q-oscillator representations used previously. We derive generalized T-Q
relations in which 3 of these parameters shift. After a suitable restriction of
parameters, we give an explicit expression for the Q-operator of the 6-vertex
model and show the connection with Baxter's expression for the central block of
his corresponding operator.Comment: 22 pages, Latex2e. This replacement is a revised version that
includes a simple explicit expression for the Q matrix for the 6-vertex mode
Extended Scaling for the high dimension and square lattice Ising Ferromagnets
In the high dimension (mean field) limit the susceptibility and the second
moment correlation length of the Ising ferromagnet depend on temperature as
chi(T)=tau^{-1} and xi(T)=T^{-1/2}tau^{-1/2} exactly over the entire
temperature range above the critical temperature T_c, with the scaling variable
tau=(T-T_c)/T. For finite dimension ferromagnets temperature dependent
effective exponents can be defined over all T using the same expressions. For
the canonical two dimensional square lattice Ising ferromagnet it is shown that
compact "extended scaling" expressions analogous to the high dimensional limit
forms give accurate approximations to the true temperature dependencies, again
over the entire temperature range from T_c to infinity. Within this approach
there is no cross-over temperature in finite dimensions above which
mean-field-like behavior sets in.Comment: 6 pages, 6 figure
General scalar products in the arbitrary six-vertex model
In this work we use the algebraic Bethe ansatz to derive the general scalar
product in the six-vertex model for generic Boltzmann weights. We performed
this calculation using only the unitarity property, the Yang-Baxter algebra and
the Yang-Baxter equation. We have derived a recurrence relation for the scalar
product. The solution of this relation was written in terms of the domain wall
partition functions. By its turn, these partition functions were also obtained
for generic Boltzmann weights, which provided us with an explicit expression
for the general scalar product.Comment: 24 page
Critical and Multicritical Semi-Random (1+d)-Dimensional Lattices and Hard Objects in d Dimensions
We investigate models of (1+d)-D Lorentzian semi-random lattices with one
random (space-like) direction and d regular (time-like) ones. We prove a
general inversion formula expressing the partition function of these models as
the inverse of that of hard objects in d dimensions. This allows for an exact
solution of a variety of new models including critical and multicritical
generalized (1+1)-D Lorentzian surfaces, with fractal dimensions ,
k=1,2,3,..., as well as a new model of (1+2)-D critical tetrahedral complexes,
with fractal dimension . Critical exponents and universal scaling
functions follow from this solution. We finally establish a general connection
between (1+d)-D Lorentzian lattices and directed-site lattice animals in (1+d)
dimensions.Comment: 44 pages, 15 figures, tex, harvmac, epsf, references adde
Bethe Equations "on the Wrong Side of Equator"
We analyse the famous Baxter's equations for () spin chain
and show that apart from its usual polynomial (trigonometric) solution, which
provides the solution of Bethe-Ansatz equations, there exists also the second
solution which should corresponds to Bethe-Ansatz beyond . This second
solution of Baxter's equation plays essential role and together with the first
one gives rise to all fusion relations.Comment: 13 pages, original paper was spoiled during transmissio
Finite temperature results on the 2d Ising model with mixed perturbation
A numerical study of finite temperature features of thermodynamical
observables is performed for the lattice 2d Ising model. Our results support
the conjecture that the Finite Size Scaling analysis employed in the study of
integrable perturbation of Conformal Field Theory is still valid in the present
case, where a non-integrable perturbation is considered.Comment: 9 pages, Latex, added references and improved introductio
A possible combinatorial point for XYZ-spin chain
We formulate and discuss a number of conjectures on the ground state vectors
of the XYZ-spin chains of odd length with periodic boundary conditions and a
special choice of the Hamiltonian parameters. In particular, arguments for the
validity of a sum rule for the components, which describes in a sense the
degree of antiferromagneticity of the chain, are given.Comment: AMSLaTeX, 15 page
Critical and Tricritical Hard Objects on Bicolorable Random Lattices: Exact Solutions
We address the general problem of hard objects on random lattices, and
emphasize the crucial role played by the colorability of the lattices to ensure
the existence of a crystallization transition. We first solve explicitly the
naive (colorless) random-lattice version of the hard-square model and find that
the only matter critical point is the non-unitary Lee-Yang edge singularity. We
then show how to restore the crystallization transition of the hard-square
model by considering the same model on bicolored random lattices. Solving this
model exactly, we show moreover that the crystallization transition point lies
in the universality class of the Ising model coupled to 2D quantum gravity. We
finally extend our analysis to a new two-particle exclusion model, whose
regular lattice version involves hard squares of two different sizes. The exact
solution of this model on bicolorable random lattices displays a phase diagram
with two (continuous and discontinuous) crystallization transition lines
meeting at a higher order critical point, in the universality class of the
tricritical Ising model coupled to 2D quantum gravity.Comment: 48 pages, 13 figures, tex, harvmac, eps
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