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

Massimo Campostrini·Paolo Rossi·Ettore Vicari
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Abstract

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 $ξ$. Several lattice formulations are compared and shown to enjoy scaling for $ξ$ as small as $2.5$. Asymptotic scaling is investigated using as bare coupling constant both the usual $β$ and $β_E$ (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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Massimo Campostrini, Paolo Rossi, Ettore Vicari. 1992-10-08. Scaling and asymptotic scaling in two-dimensional $CP^{N-1}$ models. https://doi.org/10.1016/0920-5632(93)90333-2

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