Pathologies of the large- N limit for RPN-1 , CPN-1 , QPN-1 and mixed isovector/isotensor σ -models
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 pathol...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
| Published: |
2001
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| Summary: | 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. |
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