Scaling and asymptotic scaling in two-dimensional $CP^{N-1}$ models

Details Scaling and asymptotic scaling in two-dimensional $CP^{N-1}$ models Scaling and asymptotic scaling in two-dimensional $CP^{N-1}$ models

1992-10-08

arxiv.org/abs/hep-lat/9210010v1

Nucl. Phys. Proc. Suppl. 30 (1993) 819

Physics

High Energy Physics

High Energy Physics - Lattice

5 pages + 12 figures (PostScript), report no. IFUP-TH 46/92

Scientific paper

10.1016/0920-5632(93)90333-2

Two-dimensional $CP^{N-1}$ models are investigated by Monte Carlo methods on the lattice, for values of $N$ ranging from 2 to 21. Scaling and rotation invariance are studied by comparing different definitions of correlation length $\xi$. Several lattice formulations are compared and shown to enjoy scaling for $\xi$ as small as $2.5$. Asymptotic scaling is investigated using as bare coupling constant both the usual $\beta$ and $\beta_E$ (related to the internal energy); the latter is shown to improve asymptotic scaling properties. Studies of finite size effects show their $N$-dependence to be highly non-trivial, due to the increasing radius of the $\bar z z$ bound states at large $N$.

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