970 research outputs found
Spontaneous magnetization of the XXZ Heisenberg spin-1/2 chain
Determinant representations of form factors are used to represent the
spontaneous magnetization of the Heisenberg XXZ chain (Delta >1) on the finite
lattice as the ratio of two determinants. In the thermodynamic limit (the
lattice of infinite length), the Baxter formula is reproduced in the framework
of Algebraic Bethe Ansatz. It is shown that the finite size corrections to the
Baxter formula are exponentially small.Comment: 18 pages, Latex2
An Asymptotic Expansion and Recursive Inequalities for the Monomer-Dimer Problem
Let (lambda_d)(p) be the p monomer-dimer entropy on the d-dimensional integer
lattice Z^d, where p in [0,1] is the dimer density. We give upper and lower
bounds for (lambda_d)(p) in terms of expressions involving (lambda_(d-1))(q).
The upper bound is based on a conjecture claiming that the p monomer-dimer
entropy of an infinite subset of Z^d is bounded above by (lambda_d)(p). We
compute the first three terms in the formal asymptotic expansion of
(lambda_d)(p) in powers of 1/d. We prove that the lower asymptotic matching
conjecture is satisfied for (lambda_d)(p).Comment: 15 pages, much more about d=1,2,
On the quantum inverse scattering problem
A general method for solving the so-called quantum inverse scattering problem
(namely the reconstruction of local quantum (field) operators in term of the
quantum monodromy matrix satisfying a Yang-Baxter quadratic algebra governed by
an R-matrix) for a large class of lattice quantum integrable models is given.
The principal requirement being the initial condition (R(0) = P, the
permutation operator) for the quantum R-matrix solving the Yang-Baxter
equation, it applies not only to most known integrable fundamental lattice
models (such as Heisenberg spin chains) but also to lattice models with
arbitrary number of impurities and to the so-called fused lattice models
(including integrable higher spin generalizations of Heisenberg chains). Our
method is then applied to several important examples like the sl(n) XXZ model,
the XYZ spin-1/2 chain and also to the spin-s Heisenberg chains.Comment: Latex, 20 page
Form factors of the XXZ Heisenberg spin-1/2 finite chain
Form factors for local spin operators of the XXZ Heisenberg spin-1/2 finite
chain are computed. Representation theory of Drinfel'd twists for the sl2
quantum affine algebra in finite dimensional modules is used to calculate
scalar products of Bethe states (leading to Gaudin formula) and to solve the
quantum inverse problem for local spin operators in the finite XXZ chain.
Hence, we obtain the representation of the n-spin correlation functions in
terms of expectation values(in ferromagnetic reference state) of the operator
entries of the quantum monodromy matrix satisfying Yang-Baxter algebra. This
leads to the direct calculation of the form factors of the XXZ Heisenberg
spin-1/2 finite chain as determinants of usual functions of the parameters of
the model. A two-point correlation function for adjacent sites is also derived
using similar techniques.Comment: 30 pages, LaTeX2
Correlation functions of the XXZ Heisenberg spin-1/2 chain in a magnetic field
Using the algebraic Bethe ansatz method, and the solution of the quantum
inverse scattering problem for local spins, we obtain multiple integral
representations of the -point correlation functions of the XXZ Heisenberg
spin- chain in a constant magnetic field. For zero magnetic field,
this result agrees, in both the massless and massive (anti-ferromagnetic)
regimes, with the one obtained from the q-deformed KZ equations (massless
regime) and the representation theory of the quantum affine algebra together with the corner transfer matrix approach (massive
regime).Comment: Latex2e, 26 page
Singularities in ternary mixtures of k-core percolation
Heterogeneous k-core percolation is an extension of a percolation model which
has interesting applications to the resilience of networks under random damage.
In this model, the notion of node robustness is local, instead of global as in
uniform k-core percolation. One of the advantages of k-core percolation models
is the validity of an analytical mathematical framework for a large class of
network topologies. We study ternary mixtures of node types in random networks
and show the presence of a new type of critical phenomenon. This scenario may
have useful applications in the stability of large scale infrastructures and
the description of glass-forming systems.Comment: To appear in Complex Networks, Studies in Computational Intelligence,
Proceedings of CompleNet 201
Sequential cavity method for computing free energy and surface pressure
We propose a new method for the problems of computing free energy and surface
pressure for various statistical mechanics models on a lattice . Our
method is based on representing the free energy and surface pressure in terms
of certain marginal probabilities in a suitably modified sublattice of .
Then recent deterministic algorithms for computing marginal probabilities are
used to obtain numerical estimates of the quantities of interest. The method
works under the assumption of Strong Spatial Mixing (SSP), which is a form of a
correlation decay.
We illustrate our method for the hard-core and monomer-dimer models, and
improve several earlier estimates. For example we show that the exponent of the
monomer-dimer coverings of belongs to the interval ,
improving best previously known estimate of (approximately)
obtained in \cite{FriedlandPeled},\cite{FriedlandKropLundowMarkstrom}.
Moreover, we show that given a target additive error , the
computational effort of our method for these two models is
\emph{both} for free energy and surface pressure. In
contrast, prior methods, such as transfer matrix method, require
computation effort.Comment: 33 pages, 4 figure
Three loop anomalous dimensions of twist-3 gauge operators in N=4 SYM
We propose a closed expression for the three loop anomalous dimension of a
class of twist-3 operators built with gauge fields and covariant derivatives.
To this aim, we solve the long-range Bethe Ansatz equations at finite spin and
provide a consistent analytical formula obtained assuming maximal
transcendentality violation as suggested by the known one-loop anomalous
dimension. The final result reproduces the universal cusp anomalous dimension
and obeys recursion relations inspired by the principle of reciprocity
invariance.Comment: 20 pages, JHEP styl
Moving Atom-Field Interaction: Correction to Casimir-Polder Effect from Coherent Back-action
The Casimir-Polder force is an attractive force between a polarizable atom
and a conducting or dielectric boundary. Its original computation was in terms
of the Lamb shift of the atomic ground state in an electromagnetic field (EMF)
modified by boundary conditions along the wall and assuming a stationary atom.
We calculate the corrections to this force due to a moving atom, demanding
maximal preservation of entanglement generated by the moving atom-conducting
wall system. We do this by using non-perturbative path integral techniques
which allow for coherent back-action and thus can treat non-Markovian
processes. We recompute the atom-wall force for a conducting boundary by
allowing the bare atom-EMF ground state to evolve (or self-dress) into the
interacting ground state. We find a clear distinction between the cases of
stationary and adiabatic motions. Our result for the retardation correction for
adiabatic motion is up to twice as much as that computed for stationary atoms.
We give physical interpretations of both the stationary and adiabatic atom-wall
forces in terms of alteration of the virtual photon cloud surrounding the atom
by the wall and the Doppler effect.Comment: 16 pages, 2 figures, clarified discussions; to appear in Phys. Rev.
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