Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2000-11-07
Nucl.Phys. B601 (2001) 425-502
Physics
High Energy Physics
High Energy Physics - Lattice
LaTeX, 88 pages, 33 figures
Scientific paper
10.1016/S0550-3213(01)00065-7
We compute the phase diagram in the N\to\infty limit for lattice RP^{N-1}, CP^{N-1} and QP^{N-1} sigma-models with the quartic action, and more generally for mixed isovector/isotensor models. We show that the N=\infty 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\to\infty. 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 sigma-models, and we obtain some new results concerning the complex zeros of confluent hypergeometric functions.
Sokal Alan D.
Starinets Andrei O.
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