New Universality Classes for Two-Dimensional $σ$-Models

Details New Universality Classes for Two-Dimensional $σ$-Models New Universality Classes for Two-Dimensional $σ$-Models

1993-07-31

arxiv.org/abs/hep-lat/9307022v1

Phys.Rev.Lett. 71 (1993) 3906-3909

Physics

High Energy Physics

High Energy Physics - Lattice

10 pages (includes 2 figures), 211176 bytes Postscript, NYU-TH-93/07/03, IFUP-TH 34/93

Scientific paper

10.1103/PhysRevLett.71.3906

We argue that the two-dimensional $O(N)$-invariant lattice $\sigma$-model with mixed isovector/isotensor action has a one-parameter family of nontrivial continuum limits, only one of which is the continuum $\sigma$-model constructed by conventional perturbation theory. We test the proposed scenario with a high-precision Monte Carlo simulation for $N=3,4$ on lattices up to $512 \times 512$, using a Wolff-type embedding algorithm. [CPU time $\approx$ 7 years IBM RS-6000/320H] The finite-size-scaling data confirm the existence of the predicted new family of continuum limits. In particular, the $RP^{N-1}$ and $N$-vector models do not lie in the same universality class.

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