Short-range correlations in percolation at criticality

Abstract

We derive the critical nearest-neighbor connectivity g n as 3/4, 3(7 − 9p , implying the exact value g nn = 11/16. We also determine the connectivity on a free surface as g surf n = 0.625 000 1(13) and conjecture that this value is exactly equal to 5/8. In addition, we find that at criticality, the connectivities depend on the linear finite size L as ∼ L yt −d , and the associated specific-heat-like quantities C n and C nn scale as, where d is the lattice dimensionality, y t = 1/ν the thermal renormalization exponent, and L 0 a nonuniversal constant. We provide an explanation of this logarithmic factor within the theoretical framework reported recently by Vasseur et al.

Medium effects in λK + pair production by 2.83 GeV protons on nuclei

“…In both Refs. [51] and [19], similar behavior was found for the Λ potential at normal nuclear matter density: it is attractive and increases monotonically with the growth of Λ momentum. The Λ single-particle potential in isospin symmetric and asymmetric nuclear matter at finite momenta up to 0.6 GeV/c has been also investigated recently in Ref.…”

“…The momentum dependence of this potential was studied in Ref. [51] within the framework of the relativistic Brueckner-Hartree-Fock theory, employing two kinds of Y N phenomenological potentials -Juelich 94a and Juelich 05 -constructed with the meson-exchange model by the Juelich group, at the same Λ momenta as in Ref. [50], and as in Ref.…”

Percolation thresholds and fractal dimensions for square and cubic lattices with long-range correlated defects

“…where ν a is given by Eq. (2) with ν the correlation-length exponent for uncorrelated percolation (0.8764(12) [40], 0.8762(12) [41], 0.8751(11) [42]). In practice, the correction to Eq.…”

Percolation on an isotropically directed lattice

“…While standard percolation represents one of the simplest models for investigating critical phenomena in equilibrium statistical physics [2], directed percolation has become a paradigmatic model for investigating non equilibrium phase transitions [3]. Moreover, it has been shown that the isotropic case, where bonds in both opposite directions are present with the same probability is a very particular case, with any amount of anisotropy driving the system into the same universality class as that of directed percolation [10,13,33].…”