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• W1984971186 endingPage "1917" @default.
• W1984971186 startingPage "1910" @default.
• W1984971186 abstract "High-resolution x-ray scattering and ac-calorimetric measurements have been carried out near the nematic--smectic-${mathit{A}}_{1}$ phase transition of the pure liquid-crystal compound octyloxyphenylnitrobenzoyl- oxy benzoate (${mathrm{DB}}_{8}$${mathrm{ONO}}_{2}$). Several forms of the structure factor S(q) for fitting the x-ray line shape have been tested. The critical temperature dependences of the resulting longitudinal and transverse correlation lengths ${ensuremath{xi}}_{mathrm{ensuremath{parallel}}}$ and ${ensuremath{xi}}_{mathrm{ensuremath{perp}}}$ and the smectic susceptibility ensuremath{sigma} are insensitive to the detailed form of reasonable choices for S(q). The behaviors of ${ensuremath{xi}}_{mathrm{ensuremath{parallel}}}$, ${ensuremath{xi}}_{mathrm{ensuremath{perp}}}$, and ensuremath{sigma} are analyzed here in terms of pure power laws; the effective critical exponents for the reduced temperature range 2ifmmodetimeselsetexttimesfi{}${10}^{mathrm{ensuremath{-}}5}$--1.2ifmmodetimeselsetexttimesfi{}${10}^{mathrm{ensuremath{-}}2}$ are ${ensuremath{nu}}_{mathrm{ensuremath{parallel}}}$=0.69ifmmodepmelsetextpmfi{}0.03, ${ensuremath{nu}}_{mathrm{ensuremath{perp}}}$=0.59ifmmodepmelsetextpmfi{}0.03, and ensuremath{gamma}=1.28ifmmodepmelsetextpmfi{}0.05. Although ${ensuremath{nu}}_{mathrm{ensuremath{parallel}}}$ and ensuremath{gamma} are quite close to three-dimensional (3D) XY values, the system is anisotropic with ${ensuremath{nu}}_{mathrm{ensuremath{parallel}}}$-${ensuremath{nu}}_{mathrm{ensuremath{perp}}}$=0.10ifmmodepmelsetextpmfi{}0.03. The heat-capacity data are analyzed using a nonasymptotic power-law expression with first- and second-order corrections-to-scaling terms. This analysis yields a critical exponent ensuremath{alpha} which agrees with 3D XY theory: ensuremath{alpha}=-0.007ifmmodepmelsetextpmfi{}0.003. Thus, anisotropic hyperscaling (ensuremath{alpha}+${ensuremath{nu}}_{mathrm{ensuremath{parallel}}}$+2${ensuremath{nu}}_{mathrm{ensuremath{perp}}}$=2) appears to be violated if effective exponents based on pure power-law fits to x-ray data are used. However, hyperscaling can be recovered by a preasymptotic XY analysis of the x-ray data, as shown in paper II [Phys. Rev. E 47, 1918 (1993)]." @default.
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• W1984971186 title "Critical behavior at nematic–smectic-<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=italic>A</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>phase transitions. I. High-resolution x-ray-scattering and calorimetric study of the liquid-crystal octyloxyphenylnitrobenzoyloxy benzoate" @default.
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• W1984971186 doi "https://doi.org/10.1103/physreve.47.1910" @default.
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