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This movement keeps each vertex connectivity unaltered. Besides, a transformation and its opposite are equally probable. As a consequence the detailed balance condition is satisfied with respect to the uniform measure on the ensemble of fixed connectivity graphs. A standard theorem ensures that the equilibrium state of this Markov chain is the uniform measure over the subset of fixed connectivity hypercubes reachable from the initial condition by means of plaquette transformations.
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This movement keeps each vertex connectivity unaltered. Besides, a transformation and its opposite are equally probable. As a consequence the detailed balance condition is satisfied with respect to the uniform measure on the ensemble of fixed connectivity graphs. A standard theorem ensures that the equilibrium state of this Markov chain is the uniform measure over the subset of fixed connectivity hypercubes reachable from the initial condition by means of plaquette transformations.
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77955177732
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), until the i2 th component is nonzero. The sought length is just the minimum value of t that fulfills the stopping condition.
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), until the i 2 th component is nonzero. The sought length is just the minimum value of t that fulfills the stopping condition.
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77955185068
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We say that a graph is a tree-graph if, once the link between two neighboring spins is removed, there is no way of joining them following any other path.
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We say that a graph is a tree-graph if, once the link between two neighboring spins is removed, there is no way of joining them following any other path.
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We store configurations at times 2n + 2m, with n,m integers. We?calculate the correlation function for all (t, tw ) with power of 2, allowed by the simulation length.
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We store configurations at times 2 n + 2 m, with n, m integers. We calculate the correlation function for all (t, t w) with power of 2, allowed by the simulation length.
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In the SG phase this is true only for t? tw (Ref.).
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In the SG phase this is true only for t ? t w (Ref.).
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Using gauge transformation , it is possible to rewrite an ordered configuration (by an external magnetic field, for instance) as the spin configuration found at time tw after a random start.
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Using gauge transformation, it is possible to rewrite an ordered configuration (by an external magnetic field, for instance) as the spin configuration found at time t w after a random start.
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77955195055
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Weak ergodicity breaking implies that f (α>1 ) =0.
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Weak ergodicity breaking implies that f (α > 1) = 0.
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