Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Frustrated classical Heisenberg and XY models in 2 dimensions with
  nearest neighbor exchange: exact solution for the ground state phase diagram   The ground state phase diagram is determined exactly for the frustrated
classical Heisenberg model plus nearest-neighbor biquadratic exchange
interactions on a 2-dimensional lattice. A square- and a rhombic-symmetry
version are considered. There appear ferromagnetic, incommensurate-spiral,
"up-up-down-down" (uudd) and canted ferromagnetic states, a non-spiral coplanar
state that is an ordered vortex lattice, plus a non-coplanar ordered state (a
"conical vortex lattice"). In the rhombic case, which adds biquadratic terms to
the Heisenberg model used widely for insulating manganites, the uudd state
found is the E-type state observed; this along with accounting essentially for
the variety of ground states found in these materials, shows that this model
probably contains the long-sought mechanism behind the uudd state.

2
The categories of this paper are: math
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc