## Abstract

The structure factor associated with general biquadratic correlation functions is calculated for an n-component order parameter using ε-expansion techniques in d = 4 - εdimensions. 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 ξ̂=ξ̂_{0}[(T-T_{C})/T_{C}]^{-v}, with the same n-dependent exponent v as for the correlation length characterizing fluctuations of the primary order parameter, which is denoted by ξ. The amplitude ratio X̂ = (ξ̂_{0}/ξ_{0})^{2} is universal, and we obtain X_{T}= γ_{T}/6γ+O(ε^{3}) for quadratic order parameters transforming like a traceless spin tensor in n-component space (with γ_{T} characterizing the divergence of the corresponding susceptibility) and X_{E}= α/6γ+O(ε^{3}) for energy-energy correlations, where α and γ 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 _{T} with n=2 and takes the value X_{2}= ε/20-ε^{2}/100+0(ε^{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-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.

Original language | English |
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Pages (from-to) | 2267-2278 |

Number of pages | 12 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 55 |

Issue number | 3 SUPPL. A |

DOIs | |

State | Published - 1 Jan 1997 |

Externally published | Yes |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics