## Abstract

A theory is presented for the determination of the transition temperature T_{c} for spin-^{1}/_{2} Ising models on cubic lattices with pair (J_{2}) and quartet (J_{4}) interactions. A linear relationship between T_{c} and J_{4}/J_{2} is found to have a base wider in scope than that of previous theories. The calculation of the linear coefficient is performed through the derivation of a new equation for special four-spin correlation functions which is solved in a novel way by the use of a ratio approximation. The results are compared with those derived from previous theories, series analysis and Monte Carlo calculations which are also presented here. The linear coefficient is shown to depend on a parameter which turns out to have approximately the same value for all cubic lattices, thus suggesting a set of scaled variables in terms of which the phase boundary for all cubic lattices may be fitted by a common curve. From the authors' work a coherent picture emerges for the phase behaviour of cubic Ising lattices with pair and quartet interactions, involving regions of continuous and first-order transitions separated by a tricritical point which occurs at the same value of the scaled variables for all cubic lattices.

Original language | English |
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Journal | Journal of Physics C: Solid State Physics |

Volume | 16 |

Issue number | 13 |

Pages (from-to) | 2481-2496 |

Number of pages | 16 |

ISSN | 0022-3719 |

DOIs | |

Publication status | Published - 1983 |

Externally published | Yes |