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arXiv · hep-lat/9307022

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

Sergio Caracciolo·Robert G. Edwards·Andrea Pelissetto·Alan D. Sokal
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Abstract

We argue that the two-dimensional $O(N)$-invariant lattice $σ$-model with mixed isovector/isotensor action has a one-parameter family of nontrivial continuum limits, only one of which is the continuum $σ$-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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Sergio Caracciolo, Robert G. Edwards, Andrea Pelissetto, Alan D. Sokal. 1993-07-31. New Universality Classes for Two-Dimensional $σ$-Models. https://doi.org/10.1103/physrevlett.71.3906

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