### Abstract

At zero temperature magnetic phases of the quantum spin-1/2 Heisenberg antiferromagnet on a simple cubic lattice with competing first and second neighbor exchanges (J_{1} and J_{2}) is investigated using the non-linear spin wave theory. We find existence of two phases: a two sublattice Néel phase for small J_{2} (AF), and a collinear antiferromagnetic phase at large J_{2} (CAF). We obtain the sublattice magnetizations and ground state energies for the two phases and find that there exists a first order phase transition from the AF-phase to the CAF-phase at the critical transition point, p_{c} = 0.56 or J_{2}/J_{1} = 0.28. We also show that the quartic 1/S corrections due spin-wave interactions enhance the sublattice magnetization in both the phases which causes the intermediate paramagnetic phase predicted from linear spin wave theory to disappear.

Original language | English (US) |
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Pages (from-to) | 714-726 |

Number of pages | 13 |

Journal | Journal of Statistical Physics |

Volume | 139 |

Issue number | 4 |

DOIs | |

State | Published - May 1 2010 |

### Keywords

- Frustrated magnetic spin systems
- Heisenberg spin systems
- Magnetism
- Quantum phase transition

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics