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

Journal article

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. © 2001 Elsevier Science B.V.

Authors: Sokal, A; Starinets, A

• Journal: Nuclear Physics B
• Volume: 601
• Issue: 3
• Pages: 425-502
• Publication date: 2001-05-14
• DOI: 10.1016/S0550-3213(01)00065-7
• ISSN: 0550-3213
• Language: English
• Keywords: Nematic liquid crystal* N→∞ limit* 1/N expansion; RPN-1 model* CPN-1 model* QPN-1 model* N -vector model; Nonlinear σ -model; Mixed isovector/isotensor model