## Abstract

The hypothesis of universality implies that for every scaling relation among critical exponents there exists a universal ratio among the corresponding critical amplitudes. If one writes B|t|, AF|t|2, C|t|-, and 0|t|- [where t=(pc-p)pc, p being the concentration of nonzero bonds, and +(-) stands for p<pc (p>pc)] for the leading singular terms in the probability to belong to the infinite cluster, the mean number of clusters, the clusters' mean-square size, and the pair connectedness correlation length, then it is shown that the ratios AF+AF-, C+C-, AF+B-2C+,00-, and AF+(0+)d (d is the dimensionality) are universal. Similar quantities are found for the behavior at p=pc (as a function of a "ghost" field). All of these universal ratios are derived from a universal scaled equation of state, which is calculated to second order in =6-d. The (extrapolated) results are compared with available information in dimensionalities d=2, <3,4, 5, with reasonable agreements. The amplitude relations become exact at d=6, when logarithmic corrections appear. Additional universal ratios are obtained for the confluent correction to scaling terms.

Original language | English |
---|---|

Pages (from-to) | 400-414 |

Number of pages | 15 |

Journal | Physical Review B |

Volume | 22 |

Issue number | 1 |

DOIs | |

State | Published - 1 Jan 1980 |

Externally published | Yes |

## ASJC Scopus subject areas

- Condensed Matter Physics