Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Possible Failure of Asymptotic Freedom in Two-Dimensional $RP^2$ and
  $RP^3$ $\sigma$-Models   We have simulated the two-dimensional $RP^2$ and $RP^3$ $\sigma$-models, at
correlation lengths up to about 220 (resp.\ 30), using a Wolff-type embedding
algorithm. We see no evidence of asymptotic scaling. Indeed, the data rule out
the conventional asymptotic scaling scenario at all correlation lengths less
than about $10^{9}$ (resp.\ $10^{5}$). Moreover, they are consistent with a
critical point at $\beta \approx 5.70$ (resp.\ 6.96), only 2\% (resp.\ 5\%)
beyond the largest $\beta$ at which we ran. Preliminary studies of a mixed
$S^{N-1}/RP^{N-1}$ model (i.e. isovector + isotensor action) show a similar
behavior when $\beta_T \to \infty$ with $\beta_V$ fixed $\ltapprox 0.6$, while
they are consistent with conventional asymptotic freedom along the lines
$\beta_T/\beta_V$ fixed $\ltapprox 2$. Taken as a whole, the data cast doubt on
(though they do not completely exclude) the idea that $RP^{N-1}$ and $S^{N-1}$
$\sigma$-models lie in the same universality class.

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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an