Renormalized coupling constants and related amplitude ratios for Ising systems

Using modern estimates and exact values of critical points and exponents for Ising systems, existing series expansions for various lattices are analyzed to estimate the universal amplitude ratio R(0) = (C-4(+))(2)/C+C6+, where C-+/- are the amplitudes of divergence of the susceptibility chi, above and below T-c, while C-k(+/-) are, similarly, the amplitudes for (partial derivative(k-2)chi/partial derivative h(h = 0)(k-2), we obtain R(0) = 0.1582 +/- 0.002 for d = 2 dimensions and 0.1275 +/- 0.0003 for d = 3. Similarly, we find the universal ratio C-4(+)/C-4(-) = -9.0 +/- 0.3 and -121.5 +/- 0.5 for d = 3 and 2, respectively. On using existing estimates for C+, for the second-moment correlation-length amplitude f(1)(+), and for the universal ratios C+/C- and f(1)(+)/f(1)(-), we estimate the renormalized coupling constants to be g(+)* = G(1)(+) = -C-4(+)/(C+)(2)(f(1)(+)a)(d)/upsilon(0) = 24.45 +/- 0.15 for d = 3 and 14.700 +/- 0.017 for d = 2. Beneath T-c we find G(1)(-) = -501 +/- 60, -1768 +/- 80 and -C3-B/(C-)(2) = 6.4(7) +/- 0.2, 33.0(6) +/- 0.1, where B is the spontaneous-magnetization amplitude, and thence g(-)* similar or equal to 85 and 23 for d = 3 and 2, respectively.