2010
DOI: 10.1103/physreve.81.011133
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Majority-vote model on hyperbolic lattices

Abstract: We study the critical properties of a non-equilibrium statistical model, the majority-vote model, on heptagonal and dual heptagonal lattices. Such lattices have the special feature that they only can be embedded in negatively curved surfaces. We find, by using Monte Carlo simulations and finite-size analysis, that the critical exponents 1/ν, β/ν and γ/ν are different from those of the majority-vote model on regular lattices with periodic boundary condition, which belongs to the same universality class as the e… Show more

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Cited by 79 publications
(121 citation statements)
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References 32 publications
(86 reference statements)
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“…Our results put beyond doubt the conjecture that critical polynomials, when they do not provide the exact critical frontier, give excellent approximations that approach the exact answer in the limit of infinite bases. In the ferromagnetic regime, we were able to locate critical couplings on the kagome, (4,8 2 ) and (3, 12 2 ) lattices for q = 3 and q = 4 with accuracy rivaling or exceeding that of traditional Monte Carlo or transfer matrix diagonalisation methods. Moreover, the polynomial estimates for q = 3 are comparable in precision to those for q = 4, and thus appear not to suffer from the logarithmic corrections to scaling that plague standard numerical techniques for q = 4.…”
Section: Discussionmentioning
confidence: 95%
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“…Our results put beyond doubt the conjecture that critical polynomials, when they do not provide the exact critical frontier, give excellent approximations that approach the exact answer in the limit of infinite bases. In the ferromagnetic regime, we were able to locate critical couplings on the kagome, (4,8 2 ) and (3, 12 2 ) lattices for q = 3 and q = 4 with accuracy rivaling or exceeding that of traditional Monte Carlo or transfer matrix diagonalisation methods. Moreover, the polynomial estimates for q = 3 are comparable in precision to those for q = 4, and thus appear not to suffer from the logarithmic corrections to scaling that plague standard numerical techniques for q = 4.…”
Section: Discussionmentioning
confidence: 95%
“…4 The square basis for the (4,8 2 ) lattice is shown in Figure 6. Its fundamental building block now has the expression…”
Section: Other Latticesmentioning
confidence: 99%
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