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- W1971698193 abstract "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 ${mathit{R}}_{0}$ensuremath{equiv}(${mathit{C}}_{4}^{+}$${)}^{2}$/${mathit{C}}^{+}$${mathit{C}}_{6}^{+}$, where ${mathit{C}}^{ifmmodepmelsetextpmfi{}}$ are the amplitudes of divergence of the susceptibility ensuremath{chi}, above and below ${mathit{T}}_{mathit{c}}$, while ${mathit{C}}_{mathit{k}}^{ifmmodepmelsetextpmfi{}}$ are, similarly, the amplitudes for (${mathrm{ensuremath{partial}}}^{mathit{k}mathrm{ensuremath{-}}2}$ensuremath{chi}/ensuremath{partial}${mathit{h}}^{mathit{k}mathrm{ensuremath{-}}2}$${)}_{mathit{h}=0}$; we obtain ${mathit{R}}_{0}$=0.1582ifmmodepmelsetextpmfi{}0.0002 for d=2 dimensions and 0.1275ifmmodepmelsetextpmfi{}0.0003 for d=3. Similarly, we find the universal ratio ${mathit{C}}_{4}^{+}$/${mathit{C}}_{4}^{mathrm{ensuremath{-}}}$=-9.0ifmmodepmelsetextpmfi{}0.3 and -121.5ifmmodepmelsetextpmfi{}0.5 for d=3 and 2, respectively. On using existing estimates for ${mathit{C}}^{+}$, for the second-moment correlation-length amplitude ${mathit{f}}_{1}^{+}$, and for the universal ratios ${mathit{C}}^{+}$/${mathit{C}}^{mathrm{ensuremath{-}}}$ and ${mathit{f}}_{1}^{+}$/${mathit{f}}_{1}^{mathrm{ensuremath{-}}}$, we estimate the renormalized coupling constants to be ${mathit{g}}_{+}^{mathrm{*}}$=${mathit{G}}_{1}^{+}$ensuremath{equiv}-${mathit{C}}_{4}^{+}$/(${mathit{C}}^{+}$${)}^{2}$(${mathit{f}}_{1}^{+}$a${)}^{mathit{d}}$/${mathit{v}}_{0}$=24.45ifmmodepmelsetextpmfi{}0. 15 for d=3 and 14.700ifmmodepmelsetextpmfi{}0.017 for d=2. Beneath ${mathit{T}}_{mathit{c}}$ we find ${mathit{G}}_{1}^{mathrm{ensuremath{-}}}$=-501ifmmodepmelsetextpmfi{}60, -1768ifmmodepmelsetextpmfi{}80 and -${mathit{C}}_{3}^{mathrm{ensuremath{-}}}$B/(${mathit{C}}^{mathrm{ensuremath{-}}}$${)}^{2}$=6.${4}_{7}$ifmmodepmelsetextpmfi{}0.2, 33.${0}_{6}$ifmmodepmelsetextpmfi{}0.1, where B is the spontaneous-magnetization amplitude, and thence ${mathit{g}}_{mathrm{ensuremath{-}}}^{mathrm{*}}$ensuremath{simeq}85 and 23 for d=3 and 2, respectively. textcopyright{} 1996 The American Physical Society." @default.
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- W1971698193 date "1996-08-01" @default.
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- W1971698193 title "Renormalized coupling constants and related amplitude ratios for Ising systems" @default.
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- W1971698193 doi "https://doi.org/10.1103/physreve.54.1176" @default.
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