### Abstract

We consider self-dual transverse-field Ising spin chains with [Formula Presented]-spin interaction, where the phase transition is of second and first order, for [Formula Presented] and [Formula Presented], respectively. We present a statistical analysis of the spectra of the Hamiltonians on relatively large [Formula Presented] finite lattices. Outside the critical point we found level repulsion close to the Wigner distribution and the same rigidity as for the Gaussian orthogonal ensemble. At the transition point the level statistics in the self-dual sector is shown to be the superposition of two independent Wigner distributions. This is explained by the existence of an extra symmetry, which is connected to level crossing in the thermodynamic limit. Our study has given no evidence for the possible integrability of the models for [Formula Presented], even at the transition point.

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

Pages (from-to) | 241-246 |

Number of pages | 6 |

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

Volume | 58 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 1998 |

### Fingerprint

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Physics and Astronomy(all)