### Abstract

We compute the phase diagram in the N→∞ limit for lattice RP^{N-1}, CP^{N-1} and QP^{N-1} σ-models with the quartic action, and more generally for mixed isovector/isotensor models. We show that the N=∞ limit exhibits phase transitions that are forbidden for any finite N. We clarify the origin of these pathologies by examining the exact solution of the one-dimensional model: we find that there are complex zeros of the partition function that tend to the real axis as N→∞. We conjecture the correct phase diagram for finite N as a function of the spatial dimension d. Along the way, we prove some new correlation inequalities for a class of N-component σ-models, and we obtain some new results concerning the complex zeros of confluent hypergeometric functions.

Original language | English (US) |
---|---|

Pages (from-to) | 425-502 |

Number of pages | 78 |

Journal | Nuclear Physics, Section B |

Volume | 601 |

Issue number | 3 |

DOIs | |

State | Published - May 14 2001 |

### Fingerprint

### Keywords

- Mixed isovector/isotensor model
- Nematic liquid crystal* N→∞ limit* 1/N expansion
- Nonlinear σ -model
- RP model* CP model* QP model* N -vector model

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics, Section B*,

*601*(3), 425-502. https://doi.org/10.1016/S0550-3213(01)00065-7

**Pathologies of the large- N limit for RPN-1 , CPN-1 , QPN-1 and mixed isovector/isotensor σ -models.** / Sokal, Alan D.; Starinets, Andrei O.

Research output: Contribution to journal › Article

*Nuclear Physics, Section B*, vol. 601, no. 3, pp. 425-502. https://doi.org/10.1016/S0550-3213(01)00065-7

}

TY - JOUR

T1 - Pathologies of the large- N limit for RPN-1 , CPN-1 , QPN-1 and mixed isovector/isotensor σ -models

AU - Sokal, Alan D.

AU - Starinets, Andrei O.

PY - 2001/5/14

Y1 - 2001/5/14

N2 - We compute the phase diagram in the N→∞ limit for lattice RPN-1, CPN-1 and QPN-1 σ-models with the quartic action, and more generally for mixed isovector/isotensor models. We show that the N=∞ limit exhibits phase transitions that are forbidden for any finite N. We clarify the origin of these pathologies by examining the exact solution of the one-dimensional model: we find that there are complex zeros of the partition function that tend to the real axis as N→∞. We conjecture the correct phase diagram for finite N as a function of the spatial dimension d. Along the way, we prove some new correlation inequalities for a class of N-component σ-models, and we obtain some new results concerning the complex zeros of confluent hypergeometric functions.

AB - We compute the phase diagram in the N→∞ limit for lattice RPN-1, CPN-1 and QPN-1 σ-models with the quartic action, and more generally for mixed isovector/isotensor models. We show that the N=∞ limit exhibits phase transitions that are forbidden for any finite N. We clarify the origin of these pathologies by examining the exact solution of the one-dimensional model: we find that there are complex zeros of the partition function that tend to the real axis as N→∞. We conjecture the correct phase diagram for finite N as a function of the spatial dimension d. Along the way, we prove some new correlation inequalities for a class of N-component σ-models, and we obtain some new results concerning the complex zeros of confluent hypergeometric functions.

KW - Mixed isovector/isotensor model

KW - Nematic liquid crystal N→∞ limit 1/N expansion

KW - Nonlinear σ -model

KW - RP model CP model QP model N -vector model

UR - http://www.scopus.com/inward/record.url?scp=0035858799&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035858799&partnerID=8YFLogxK

U2 - 10.1016/S0550-3213(01)00065-7

DO - 10.1016/S0550-3213(01)00065-7

M3 - Article

VL - 601

SP - 425

EP - 502

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 3

ER -