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• W1994456005 abstract "The hypothesis of universality implies that for every scaling relation among critical exponents there exists a universal ratio among the corresponding critical amplitudes. If one writes $B{|t|}^{ensuremath{beta}}$, ${{A}_{F}}^{ifmmodepmelsetextpmfi{}}{|t|}^{2ensuremath{-}ensuremath{alpha}}$, ${C}^{ifmmodepmelsetextpmfi{}}{|t|}^{ensuremath{-}ensuremath{gamma}}$, and ${ensuremath{xi}}_{0}{|t|}^{ensuremath{-}ensuremath{nu}}$ [where $t=frac{({p}_{c}ensuremath{-}p)}{{p}_{c}}$, $p$ being the concentration of nonzero bonds, and +(-) stands for $p<{p}_{c}$ ($p>{p}_{c}$)] for the leading singular terms in the probability to belong to the infinite cluster, the mean number of clusters, the clusters' mean-square size, and the pair connectedness correlation length, then it is shown that the ratios $frac{{{A}_{F}}^{+}}{{{A}_{F}}^{ensuremath{-}}}$, $frac{{C}^{+}}{{C}^{ensuremath{-}}}$, ${{A}_{F}}^{+}{B}^{ensuremath{-}2}{C}^{+}$, $frac{{ensuremath{xi}}_{0}^{+}}{{ensuremath{xi}}_{0}^{ensuremath{-}}}$, and ${{A}_{F}}^{+}{({ensuremath{xi}}_{0}^{+})}^{d}$ ($d$ is the dimensionality) are universal. Similar quantities are found for the behavior at $p={p}_{c}$ (as a function of a ghost field). All of these universal ratios are derived from a universal scaled equation of state, which is calculated to second order in $ensuremath{epsilon}=6ensuremath{-}d$. The (extrapolated) results are compared with available information in dimensionalities $d=2, 3, 4, 5$, with reasonable agreements. The amplitude relations become exact at $d=6$, when logarithmic corrections appear. Additional universal ratios are obtained for the confluent correction to scaling terms." @default.
• W1994456005 created "2016-06-24" @default.
• W1994456005 creator A5079687270 @default.
• W1994456005 date "1980-07-01" @default.
• W1994456005 modified "2023-09-27" @default.
• W1994456005 title "Universal critical amplitude ratios for percolation" @default.
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• W1994456005 doi "https://doi.org/10.1103/physrevb.22.400" @default.
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