Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Thermal Phase Transition of Generalized Heisenberg Models for SU(N)
  Spins on Square and Honeycomb Lattices   We investigate thermal phase transitions to a valence-bond solid phase in
SU(N) Heisenberg models with four- or six-body interactions on a square or
honeycomb lattice, respectively. In both cases, a thermal phase transition
occurs that is accompanied by rotational symmetry breaking of the lattice. We
perform quantum Monte Carlo calculations in order to clarify the critical
properties of the models. The estimated critical exponents indicate that the
universality classes of the square- and honeycomb-lattice cases are identical
to those of the classical $XY$ model with a $Z_4$ symmetry-breaking field and
the 3-state Potts model, respectively. In the square-lattice case, the thermal
exponent, $\nu$, monotonically increases as the system approaches the quantum
critical point, while the values of the critical exponents, $\eta$ and
$\gamma/\nu$, remain constant. From a finite-size scaling analysis, we find
that the system exhibits weak universality, because the $Z_4$ symmetry-breaking
field is always marginal. In contrast, $\nu$ in the honeycomb-lattice case
exhibits a constant value, even in the vicinity of the quantum critical point,
because the $Z_3$ field remains relevant in the SU(3) and SU(4) cases.

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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th