2,035 research outputs found
An Importance Sampling Algorithm for the Ising Model with Strong Couplings
We consider the problem of estimating the partition function of the
ferromagnetic Ising model in a consistent external magnetic field. The
estimation is done via importance sampling in the dual of the Forney factor
graph representing the model. Emphasis is on models at low temperature
(corresponding to models with strong couplings) and on models with a mixture of
strong and weak coupling parameters.Comment: Proc. 2016 Int. Zurich Seminar on Communications (IZS), Zurich,
Switzerland, March 2-4, 2016, pp. 180-18
Topological Defects on the Lattice I: The Ising model
In this paper and its sequel, we construct topologically invariant defects in
two-dimensional classical lattice models and quantum spin chains. We show how
defect lines commute with the transfer matrix/Hamiltonian when they obey the
defect commutation relations, cousins of the Yang-Baxter equation. These
relations and their solutions can be extended to allow defect lines to branch
and fuse, again with properties depending only on topology. In this part I, we
focus on the simplest example, the Ising model. We define lattice spin-flip and
duality defects and their branching, and prove they are topological. One useful
consequence is a simple implementation of Kramers-Wannier duality on the torus
and higher genus surfaces by using the fusion of duality defects. We use these
topological defects to do simple calculations that yield exact properties of
the conformal field theory describing the continuum limit. For example, the
shift in momentum quantization with duality-twisted boundary conditions yields
the conformal spin 1/16 of the chiral spin field. Even more strikingly, we
derive the modular transformation matrices explicitly and exactly.Comment: 45 pages, 9 figure
Height representation of XOR-Ising loops via bipartite dimers
The XOR-Ising model on a graph consists of random spin configurations on
vertices of the graph obtained by taking the product at each vertex of the
spins of two independent Ising models. In this paper, we explicitly relate loop
configurations of the XOR-Ising model and those of a dimer model living on a
decorated, bipartite version of the Ising graph. This result is proved for
graphs embedded in compact surfaces of genus g.
Using this fact, we then prove that XOR-Ising loops have the same law as
level lines of the height function of this bipartite dimer model. At
criticality, the height function is known to converge weakly in distribution to
a Gaussian free field.
As a consequence, results of this paper shed a light on the occurrence of the
Gaussian free field in the XOR-Ising model. In particular, they prove a
discrete analogue of Wilson's conjecture, stating that the scaling limit of
XOR-Ising loops are "contour lines" of the Gaussian free field.Comment: 41 pages, 10 figure
An algorithmic proof for the completeness of two-dimensional Ising model
We show that the two dimensional Ising model is complete, in the sense that
the partition function of any lattice model on any graph is equal to the
partition function of the 2D Ising model with complex coupling. The latter
model has all its spin-spin coupling equal to i\pi/4 and all the parameters of
the original model are contained in the local magnetic fields of the Ising
model. This result has already been derived by using techniques from quantum
information theory and by exploiting the universality of cluster states. Here
we do not use the quantum formalism and hence make the completeness result
accessible to a wide audience. Furthermore our method has the advantage of
being algorithmic in nature so that by following a set of simple graphical
transformations, one is able to transform any discrete lattice model to an
Ising model defined on a (polynomially) larger 2D lattice.Comment: 18 pages, 15 figures, Accepted for publication in Physical Review
Thermal Operators in Ising Percolation
We discuss a new cluster representation for the internal energy and the
specific heat of the d-dimensional Ising model, obtained by studying the
percolation mapping of an Ising model with an arbitrary set of
antiferromagnetic links. Such a representation relates the thermal operators to
the topological properties of the Fortuin-Kasteleyn clusters of Ising
percolation and is a powerful tool to get new exact relations on the
topological structure of FK clusters of the Ising model defined on an arbitrary
graph.Comment: 17 pages, 2 figures. Improved version. Major changes in the text and
in the notations. A missing term added in the specific heat representatio
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