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- W1971116882 abstract "Arguments are presented which allow one to characterize weak-scaling correlations in terms of thermodynamic homogeneity. Using as a guide the present indications on the spin-spin correlation function of the three-dimensional Ising model, it is argued that the thermodynamic effects of the smooth deviations from strong scaling in dimension $d>2$ can be accounted for most easily by looking at the correlations at a second effective length $ensuremath{zeta}=ensuremath{zeta}(ensuremath{omega})$, much smaller than the correlation length. This depends on a constant $ensuremath{omega}$, a nonzero value of which indicates deviation from strong scaling and $ensuremath{zeta}(ensuremath{omega})$ is determined as that length over which an effective strong-scaling correlation in dimension ($densuremath{-}ensuremath{omega}$) yields the expected scaling relation $ensuremath{gamma}=(2ensuremath{-}ensuremath{eta})ensuremath{nu}$. It is found that $ensuremath{zeta}(ensuremath{omega})$ is much larger than the second length which appears in the weak-scaling theory of Stell. The constant $ensuremath{omega}$ enters all relations between critical exponents which depend explicitly on dimensionality and it is shown that a value $ensuremath{omega}ensuremath{simeq}frac{1}{12}$ is consistent with the exponents for the three-dimensional Ising model. It is argued that weak scaling should be expected for general pair correlations and it is shown how a further inequality between critical exponents involving energy-density correlations can be derived. The limitation of our scheme to values of $d$ smaller than that at which the mean-field behavior sets in is explicitly pointed out." @default.
- W1971116882 created "2016-06-24" @default.
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- W1971116882 date "1972-07-01" @default.
- W1971116882 modified "2023-10-14" @default.
- W1971116882 title "Phenomenological Weak-Scaling Theory" @default.
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- W1971116882 doi "https://doi.org/10.1103/physrevb.6.281" @default.
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