Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: High-precision percolation thresholds and Potts-model critical manifolds
  from graph polynomials   The critical curves of the q-state Potts model can be determined exactly for
regular two-dimensional lattices G that are of the three-terminal type.
Jacobsen and Scullard have defined a graph polynomial P_B(q,v) that gives
access to the critical manifold for general lattices. It depends on a finite
repeating part of the lattice, called the basis B, and its real roots in the
temperature variable v = e^K - 1 provide increasingly accurate approximations
to the critical manifolds upon increasing the size of B. These authors computed
P_B(q,v) for large bases (up to 243 edges), obtaining determinations of the
ferromagnetic critical point v_c > 0 for the (4,8^2), kagome, and (3,12^2)
lattices to a precision (of the order 10^{-8}) slightly superior to that of the
best available Monte Carlo simulations.
  In this paper we describe a more efficient transfer matrix approach to the
computation of P_B(q,v) that relies on a formulation within the periodic
Temperley-Lieb algebra. This makes possible computations for substantially
larger bases (up to 882 edges), and the precision on v_c is hence taken to the
range 10^{-13}. We further show that a large variety of regular lattices can be
cast in a form suitable for this approach. This includes all Archimedean
lattices, their duals and their medials. For all these lattices we tabulate
high-precision estimates of the bond percolation thresholds p_c and Potts
critical points v_c. We also trace and discuss the full Potts critical manifold
in the (q,v) plane, paying special attention to the antiferromagnetic region v
< 0. Finally, we adapt the technique to site percolation as well, and compute
the polynomials P_B(p) for certain Archimedean and dual lattices (those having
only cubic and quartic vertices), using very large bases (up to 243 vertices).
This produces the site percolation thresholds p_c to a precision of the order
10^{-9}.

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The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
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The categories of this paper are: econ
8
The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org