Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A strong-coupling analysis of two-dimensional O(N) sigma models with
  N<=2 on square, triangular and honeycomb lattices   The critical behavior of two-dimensional ${\rm O}(N)$ $\sigma$ models with
$N\leq 2$ on the square, triangular, and honeycomb lattices is investigated by
an analysis of the strong-coupling expansion of the two-point fundamental
Green's function $G(x)$, calculated up to 21st order on the square lattice,
15th order on the triangular lattice, and 30th order on the honeycomb lattice.
For $N<2$ the critical behavior is of power-law type, and the exponents
$\gamma$ and $\nu$ extracted from our strong-coupling analysis confirm exact
results derived assuming universality with solvable solid-on-solid models. At
$N=2$, i.e., for the 2-$d$ XY model, the results from all lattices considered
are consistent with the Kosterlitz-Thouless exponential approach to
criticality, characterized by an exponent $\sigma=1/2$, and with universality.
The value $\sigma=1/2$ is confirmed within an uncertainty of few per cent. The
prediction $\eta=1/4$ is also roughly verified. For various values of $N\leq
2$, we determine some ratios of amplitudes concerning the two-point function
$G(x)$ in the critical limit of the symmetric phase. This analysis shows that
the low-momentum behavior of $G(x)$ in the critical region is essentially
Gaussian at all values of $N\leq 2$. New exact results for the long-distance
behavior of $G(x)$ when $N=1$ (Ising model in the strong-coupling phase)
confirm this statement.

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The categories of this paper are: math-ph
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
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The categories of this paper are: eess
35
The categories of this paper are: mtrl-th