### Abstract

We propose a mechanism that can create a mass gap in the SU(2) chiral spin model at arbitrarily small temperatures. We give a sufficient condition for the mass gap to be non-zero in terms of the behaviour of an external ℤ(2) flux introduced by twisted boundary conditions. This condition in turn is rewritten in terms of an effective dual Ising model with an external magnetic field generated by SO(3) vortices. We show that having a non-zero magnetic field in the effective Ising model is sufficient for the SU(2) system to have a mass gap. We also show that certain vortex correlation inequalities, if satisfied, would imply a non-zero effective magnetic field. Finally, we give some plausibility arguments and Monte Carlo evidence for the required correlation inequalities.

Original language | English |
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Pages (from-to) | 613-638 |

Number of pages | 26 |

Journal | Nuclear Physics B |

Volume | 482 |

Issue number | 3 |

DOIs | |

Publication status | Published - Dec 30 1996 |

### Fingerprint

### Keywords

- Confinement
- Disorder
- Lattice
- SU(2) principal chiral model

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

**SO(3) vortices as a mechanism for generating a mass gap in the 2D SU(2) principal chiral model.** / Kovács, T.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 482, no. 3, pp. 613-638. https://doi.org/10.1016/S0550-3213(96)00561-5

}

TY - JOUR

T1 - SO(3) vortices as a mechanism for generating a mass gap in the 2D SU(2) principal chiral model

AU - Kovács, T.

PY - 1996/12/30

Y1 - 1996/12/30

N2 - We propose a mechanism that can create a mass gap in the SU(2) chiral spin model at arbitrarily small temperatures. We give a sufficient condition for the mass gap to be non-zero in terms of the behaviour of an external ℤ(2) flux introduced by twisted boundary conditions. This condition in turn is rewritten in terms of an effective dual Ising model with an external magnetic field generated by SO(3) vortices. We show that having a non-zero magnetic field in the effective Ising model is sufficient for the SU(2) system to have a mass gap. We also show that certain vortex correlation inequalities, if satisfied, would imply a non-zero effective magnetic field. Finally, we give some plausibility arguments and Monte Carlo evidence for the required correlation inequalities.

AB - We propose a mechanism that can create a mass gap in the SU(2) chiral spin model at arbitrarily small temperatures. We give a sufficient condition for the mass gap to be non-zero in terms of the behaviour of an external ℤ(2) flux introduced by twisted boundary conditions. This condition in turn is rewritten in terms of an effective dual Ising model with an external magnetic field generated by SO(3) vortices. We show that having a non-zero magnetic field in the effective Ising model is sufficient for the SU(2) system to have a mass gap. We also show that certain vortex correlation inequalities, if satisfied, would imply a non-zero effective magnetic field. Finally, we give some plausibility arguments and Monte Carlo evidence for the required correlation inequalities.

KW - Confinement

KW - Disorder

KW - Lattice

KW - SU(2) principal chiral model

UR - http://www.scopus.com/inward/record.url?scp=0030607748&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030607748&partnerID=8YFLogxK

U2 - 10.1016/S0550-3213(96)00561-5

DO - 10.1016/S0550-3213(96)00561-5

M3 - Article

AN - SCOPUS:0030607748

VL - 482

SP - 613

EP - 638

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 3

ER -