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- W2048659068 abstract "The structure factor associated with general biquadratic correlation functions is calculated for an n-component order parameter using ensuremath{epsilon}-expansion techniques in d=4-ensuremath{epsilon} dimensions. The results apply to energy-energy and strain-strain correlations as well as to correlations of higher harmonics in density wave systems. We find the correlations of these secondary order parameters to be characterized by a correlation length ensuremath{xi}-|Ax=ensuremath{xi}-|${mathrm{Ax}}_{0}$[(T-${mathrm{T}}_{mathrm{c}}$)/${mathrm{T}}_{mathrm{c}}$${]}^{mathrm{ensuremath{-}}ensuremath{nu}}$, with the same n-dependent exponent ensuremath{nu} as for the correlation length characterizing fluctuations of the primary order parameter, which is denoted by ensuremath{xi}. The amplitude ratio X-|Axensuremath{equiv}(ensuremath{xi}-|${mathrm{Ax}}_{0}$/${ensuremath{xi}}_{0}$${)}^{2}$ is universal, and we obtain ${mathrm{X}}_{mathrm{T}}$=${ensuremath{gamma}}_{mathrm{T}}$/6ensuremath{gamma}+O(${mathrm{ensuremath{epsilon}}}^{3}$) for quadratic order parameters transforming like a traceless spin tensor in n-component space (with ${ensuremath{gamma}}_{mathrm{T}}$ characterizing the divergence of the corresponding susceptibility) and ${mathrm{X}}_{mathrm{E}}$=ensuremath{alpha}/6ensuremath{gamma}+O(${mathrm{ensuremath{epsilon}}}^{3}$) for energy-energy correlations, where ensuremath{alpha} and ensuremath{gamma} denote the usual specific heat and susceptibility critical exponents, respectively. The universal amplitude ratio for the second harmonic in density wave systems is given by ${mathrm{X}}_{mathrm{T}}$ with n=2 and takes the value ${mathrm{X}}_{2}$=ensuremath{epsilon}/20-${mathrm{ensuremath{epsilon}}}^{2}$/100+O(${mathrm{ensuremath{epsilon}}}^{3}$), thus being very small. This naturally explains previously puzzling experimental results for the critical behavior of the second harmonic structure factor at the nematic--smectic-${mathrm{A}}_{2}$ transition of a thermotropic liquid crystal. Applications to sound attenuation in liquids or solids close to critical transitions and to colloidal interactions in near-critical binary mixtures are briefly discussed." @default.
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- W2048659068 date "1997-03-01" @default.
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- W2048659068 title "Critical behavior of energy-energy, strain-strain, higher-harmonics,and similar correlation functions" @default.
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- W2048659068 doi "https://doi.org/10.1103/physreve.55.2267" @default.
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