## Abstract

The equations for the beta relaxation dynamics as obtained within mode-coupling theory for the glass transition are solved asymptotically for parameters near Whitney cusp singularities. The solution is given by a two-parameter scaling law, where the time t enters as ln t and where the scaling times depend exponentially with a Vogel-Fulcher like form on the control parameters. The master function is given in terms of Weierstrass' elliptic function. It describes crossovers from critical relaxation Phi (t) varies as 1/ln^{2}t to a constant f_{0}, to a power-law decay 1/t ^{a}, to Phi (t) varies as -lnt, or to Phi (t) varies as ln^{2}t depending on the sector in parameter space. The relaxation data for the Cu-Mn spin-glass alloy can be described by the theory for a time interval of eight decades.

Original language | English |
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Article number | 015 |

Pages (from-to) | 4203-4222 |

Number of pages | 20 |

Journal | Journal of Physics Condensed Matter |

Volume | 1 |

Issue number | 26 |

DOIs | |

State | Published - 1989 |

Externally published | Yes |