Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classical Ring-exchange Processes on the Triangular Lattice   The effects of the ring-exchange Hamiltonian H_3 = J_3 sum_{<ijk>} (S_i *
S_j) (S_i * S_k) on the triangular lattice are studied using classical Monte
Carlo simulations. Each spin $S_i$ is treated as a classical XY spin taking on
Q equally spaced angles (Q-states clock model). For Q=6, a first-order
transition into a stripe-ordered phase preempts the macroscopic classical
degeneracy. For Q > 6, a finite window of critical phase exists, intervening
between the low-temperature stripe phase and the high-temperature paramagnetic
phase.

21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph