Critical exponents for two-dimensional Heisenberg ferromagnet with long-range interaction

Fakioǧlu, S.

doi:10.1007/bf02455860

Cited by 2 publications

(1 citation statement)

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“…For σ < d/2 the critical indices take their MF values, for d/2 < σ < 2 they are σ-dependent, and for σ > 2 they take their short-range (SR) values. Similar investigations have been conducted * Corresponding author: cristian@mda.cinvestav.mx for Potts [13,15,16,17], Heisenberg [18,19,20,21,22,23], and other [24,25] models. The following picture is often found: for small enough decay rate µ, MF indices are obtained.…”

Section: Introductionmentioning

confidence: 56%

Shortest paths on systems with power-law distributed long-range connections

Moukarzel

Menezes

2002

Phys. Rev. E

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We discuss shortest-path lengths ℓ(r) on periodic rings of size L supplemented with an average of pL randomly located long-range links whose lengths are distributed according to P l ∼ l −µ . Using rescaling arguments and numerical simulation on systems of up to 10 7 sites, we show that a characteristic length ξ exists such that ℓ(r) ∼ r for r < ξ but ℓ(r) ∼ r θs (µ) for r >> ξ. For small p we find that the shortest-path length satisfies the scaling relation ℓ(r, µ, p)/ξ = f (µ, r/ξ). Three regions with different asymptotic behaviors are found, respectively: a) µ > 2 where θs = 1, b) 1 < µ < 2 where 0 < θs(µ) < 1/2 and, c) µ < 1 where ℓ(r) behaves logarithmically, i.e. θs = 0. The characteristic length ξ is of the form ξ ∼ p −ν with ν = 1/(2 − µ) in region b), but depends on L as well in region c). A directed model of shortest-paths is solved and compared with numerical results.

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