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Article Dans Une Revue Physical Review E Année : 2019

Observation of nonscalar and logarithmic correlations in two- and three-dimensional percolation

Résumé

In bulk percolation, we exhibit operators that insert N clusters with any given symmetry under the symmetric group SN. At the critical threshold, this leads to predictions that certain combinations of two-point correlation functions depend logarithmically on distance, without the usual power law. The behavior under rotations of certain amplitudes of correlators is also determined exactly. All these results hold in any dimension, 2≤d≤6. Moreover, in d=2 the critical exponents and universal logarithmic prefactors are obtained exactly. We test these predictions against extensive simulations of critical bond percolation in d=2 and 3, for all correlators up to N=4 (d=2) and N=3 (d=3), finding excellent agreement. In d=3 we further obtain precise numerical estimates for critical exponents and logarithmic prefactors.

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Dates et versions

hal-01891466 , version 1 (09-10-2018)

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Xiaojun Tan, Romain Couvreur, Youjin Deng, Jesper Lykke Jacobsen. Observation of nonscalar and logarithmic correlations in two- and three-dimensional percolation. Physical Review E , 2019, 99 (5), pp.050103. ⟨10.1103/PhysRevE.99.050103⟩. ⟨hal-01891466⟩
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