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- W2093645713 abstract "A duality relation derived by Jos'e, Kadanoff, Kirkpatrick, and Nelson and by Knops is exploited to calculate properties of $mathrm{XY}$ and roughening models from known properties of the dual models. It is shown that the correlation length in $mathrm{XY}$ models is exactly given by ${ensuremath{xi}}^{ensuremath{-}1}=stackrel{ifmmode tilde{}else ~{}fi{}}{ensuremath{beta}}stackrel{ifmmode tilde{}else ~{}fi{}}{f}$, where $stackrel{ifmmode tilde{}else ~{}fi{}}{f}$ is the free energy per unit length of a step and $stackrel{ifmmode tilde{}else ~{}fi{}}{ensuremath{beta}}$ is the inverse temperature in the corresponding roughening model. Similarly, the exponent $ensuremath{eta}$ below ${T}_{c}$ in an $mathrm{XY}$ model is given by $ensuremath{eta}={mathrm{lim}}_{|stackrel{ensuremath{rightarrow}}{mathrm{r}}|ensuremath{rightarrow}ensuremath{infty}}frac{stackrel{ifmmode tilde{}else ~{}fi{}}{ensuremath{beta}}{stackrel{ifmmode tilde{}else ~{}fi{}}{F}}_{1}(stackrel{ensuremath{rightarrow}}{mathrm{r}})}{ln|stackrel{ensuremath{rightarrow}}{mathrm{r}}|}$, where ${stackrel{ifmmode tilde{}else ~{}fi{}}{F}}_{1}(stackrel{ensuremath{rightarrow}}{mathrm{r}})$ is the free energy associated with two screw dislocations of unit strength and opposite sign separated by the distance $stackrel{ensuremath{rightarrow}}{mathrm{r}}$ in the corresponding roughening model." @default.
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- W2093645713 date "1978-05-01" @default.
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- W2093645713 title "Correlation functions in<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mi>XY</mml:mi></mml:math>models and step free energies in roughening models" @default.
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- W2093645713 doi "https://doi.org/10.1103/physrevb.17.3710" @default.
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