## Abstract

Starting from the exact result of Majumdar and Ghosh (1969) for the dimerized ground state of a Heisenberg S=^{1}/_{2} antiferromagnet with competing next-nearest-neighbour interaction J _{2}+1/2J_{1} on a linear chain, it is shown that this state is the ground state of the same kind of Hamiltonian, if couplings are extended up to 2n-nearest-neighbours, and the relation J_{1}=2n, J_{2}=2n-1, ..., J_{2n}=1 holds. Furthermore, it is proved rigorously that this state is the ground state when n=2 and J_{1}-2J_{2}+J _{3}=0, J_{3}=2J_{4}, in a finite interval of values of the parameter J_{4}. A rigorous lower limit for the extension of this interval is found to be 0<or=J_{4}<or=^{1}/ _{4}J_{1}. A comparison with ground-state configurations of the equivalent classical Heisenberg and Ising model is discussed.

Original language | English (US) |
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Article number | 008 |

Pages (from-to) | 445-453 |

Number of pages | 9 |

Journal | Journal of Physics: Condensed Matter |

Volume | 3 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 1991 |

## ASJC Scopus subject areas

- Materials Science(all)
- Condensed Matter Physics