Multi-range percolation model on the square lattice

Amaral, Charles S. do; Schnabel, M.; Lima, Bernardo N. B. de; Atman, A. P. F.

doi:10.1016/j.physa.2019.122383

Cited by 3 publications

(2 citation statements)

References 11 publications

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“…For the multi-range percolation model with three ranges, 1, m and u, the effective critical point varies in an irregular manner when u is fixed and m varies between 1 and u [20]. We obtain numerical evidence showing analogous behavior in the multi-range Ising model.…”

Section: Resultsmentioning

confidence: 61%

“…These authors also conjecture that convergence is monotone and nonincreasing in each variable k i . Recent numerical work suggests that, if d = 2, this conjecture is valid for n = 1 and n = 2 [20]. These results raise the question whether other models exhibiting phase transitions and having local interactions between sites (bonds), have properties similar to multi-range percolation.…”

Section: Introductionmentioning

confidence: 96%

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Multirange Ising model on the square lattice

Amaral,

de Lima,

Dickman

et al. 2019

Preprint

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We study the Ising model on Z 2 and show, via numerical simulation, that allowing interactions between spins separated by distances 1 and m (two ranges), the critical temperature, T c (m), converges monotonically to the critical temperature of the Ising model on Z 4 as m → ∞. Only interactions between spins located in directions parallel to each coordinate axis are considered. We also simulated the model with interactions between spins at distances of 1, m and u (three ranges), with u a multiple of m; in this case our results indicate that T c (m, u) converges to the critical temperature of the model on Z 6 . For percolation, analogous results were proven for the critical probability p c [B.

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Section: Resultsmentioning

confidence: 61%

Section: Introductionmentioning

confidence: 96%