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Dyson instability for 2D nonlinear O(N) sigma models
Journal article   Open access   Peer reviewed

Dyson instability for 2D nonlinear O(N) sigma models

Y Meurice
Physical review. D, Particles and fields, Vol.80(5), 054020
09/01/2009
DOI: 10.1103/PHYSREVD.80.054020
url
https://arxiv.org/pdf/0907.2980View
Open Access

Abstract

For lattice models with compact field integration (nonlinear sigma models over compact manifolds and gauge theories with compact groups) and satisfying some discrete symmetry, the change of sign of the bare coupling g{sub 0}{sup 2} at zero results in a mere discontinuity in the average energy rather than the catastrophic instability occurring in theories with integration over arbitrarily large fields. This indicates that the large order of perturbative series and the nonperturbative contributions should have unexpected features. Using the large-N limit of two-dimensional nonlinear O(N) sigma model, we discuss the complex singularities of the average energy for complex 't Hooft coupling {lambda}{sup t}=g{sub 0}{sup 2}N. A striking difference with the usual situation is the absence of the cut along the negative real axis. We show that the zeros of the partition function can only be inside a clover shape region of the complex {lambda}{sup t} plane. We calculate the density of states and use the result to verify numerically the statement about the zeros. We propose dispersive representations of the derivatives of the average energy for an approximate expression of the discontinuity. The discontinuity is purely nonperturbative and contributions at small negative coupling in one dispersive representation are essential to guarantee that the derivatives become exponentially small when {lambda}{sup t}{yields}0{sup +}. We discuss the implications for gauge theories.
 APPROXIMATIONS COMPUTERIZED SIMULATION COUPLING DENSITY GAUGE INVARIANCE INSTABILITY LATTICE FIELD THEORY NONLINEAR PROBLEMS PARTITION FUNCTIONS PHYSICS OF ELEMENTARY PARTICLES AND FIELDS SIGMA MODEL SINGULARITY SYMMETRY TWO-DIMENSIONAL CALCULATIONS

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