Self-avoiding walks in two to five dimensions: exact enumerations and series study

High-precision determination of the critical exponent γ for self-avoiding walks

“…Thus if use the value of γ given by [17], see (1), we get a value for β c in agreement with their estimate (13). However if we use our estimate of γ, we get a β c which is off by five to twenty times the stated error bars.…”

“…Using the values of c N reported in [5,17], we find β c = 0.2134987 ± 0.0000001 for δ = 1.1619 0.2134811 ± 0.0000031 for δ = 1.1576 (15) where the "error" indicates the spread of the Padè approximants we have considered.…”

Precise determination of critical exponents and equation of state by field theory methods

“…Only recently have consistent, but significantly more precise, experimental results been reported in low gravity superfluid experiments [41]. Also the precision of results coming from high temperature expansions [18][19][20][21][22][23][24][25][26][27][28][29] and various numerical simulations [30][31][32][33][34][35][36][37][38][39][40] on the lattice has kept steadily improving.…”

N-vector spin models on the simple-cubic and the body-centered-cubic lattices: A study of the critical behavior of the susceptibility and of the correlation length by high-temperature series extended to orderβ21Butera1, Comi2 1997Phys. Rev. B13591310View full textAdd to dashboardCite

“…In some cases, in particular for N = 0 in Refs. [4,47,61] and for N = 1 in Refs. [7,62], numerical work has suggested slightly different confluent exponents, which might be more accurate or, to some extent, also provide an "effective" description of higher confluent corrections.…”