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The relationship of local ordering and long-range order is studied for quasicrystalline tilings of plane and space. Two versions of the concept of local rules are introduced: strong and weak. Necessary conditions of the existence of strong local rules are found. They are mainly reduced to the constraints for irrational numbers related to(More)
A free field representation for the type I vertex operators and the corner transfer matrices of the eight-vertex model is proposed. The construction uses the vertex-face correspondence, which makes it possible to expresses correlation functions of the eight-vertex model in terms of correlation functions of the SOS model with a nonlocal insertion. This new(More)
We define a model of quantum computation with local fermionic modes (LFMs) — sites which can be either empty or occupied by a fermion. With the standard correspondence between the Foch space of m LFMs and the Hilbert space of m qubits, simulation of one fermionic gate takes O(m) qubit gates and vice versa. We show that using different encodings, the(More)
In this talk we solve continuum and discrete elasticity problems in infinite domains by introducing exact artificial boundary conditions (ABCs) that can be applied at a planar interface below which there are no forces. The problem domain is assumed to be composed of a large regular domain, which can be handled analytically, and a small irregular region,(More)