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The ability to distribute quantum entanglement is a prerequisite for many fundamental tests of quantum theory and numerous quantum information protocols. Two distant parties can increase the amount of entanglement between them by means of quantum communication encoded in a carrier that is sent from one party to the other. Intriguingly, entanglement can be… (More)
We calculate very long low-and high-temperature series for the susceptibility χ of the square lattice Ising model as well as very long series for the five-particle contribution χ (5) and six-particle contribution χ (6). These calculations have been made possible by the use of highly optimized polynomial time modular algorithms and a total of more than… (More)
We present a simple, but efficient, way to calculate connection matrices between sets of independent local solutions, defined at two neighboring singular points, of Fuchsian differential equations of quite large orders, such as those found for the third and fourth contribution (χ (3) and χ (4)) to the magnetic susceptibility of square lattice Ising model.… (More)
We give an example of infinite order rational transformation that leaves a linear differential equation covariant. This example can be seen as a non-trivial but still simple illustration of an exact representation of the renormalization group.
We analyze free-fermion conditions on vertex models. We show –by examining examples of vertex models on square, triangular, and cubic lattices– how they amount to degeneration conditions for known symmetries of the Boltz-mann weights, and propose a general scheme for such a process in two and more dimensions.
We consider some two-dimensional birational transformations. One of them is a birational deformation of the Hénon map. For some of these birational mappings, the post critical set (i.e. the iterates of the critical set) is infinite and we show that this gives straightforwardly the algebraic covariant curves of the transformation when they exist. These… (More)