Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transfer Matrices for the Partition Function of the Potts Model on
  Toroidal Lattice Strips   We present a method for calculating transfer matrices for the $q$-state Potts
model partition functions $Z(G,q,v)$, for arbitrary $q$ and temperature
variable $v$, on strip graphs $G$ of the square (sq), triangular (tri), and
honeycomb (hc) lattices of width $L_y$ vertices and of arbitrarily great length
$L_x$ vertices, subject to toroidal and Klein bottle boundary conditions. For
the toroidal case we express the partition function as $Z(\Lambda, L_y \times
L_x,q,v) = \sum_{d=0}^{L_y} \sum_j b_j^{(d)} (\lambda_{Z,\Lambda,L_y,d,j})^m$,
where $\Lambda$ denotes lattice type, $b_j^{(d)}$ are specified polynomials of
degree $d$ in $q$, $\lambda_{Z,\Lambda,L_y,d,j}$ are eigenvalues of the
transfer matrix $T_{Z,\Lambda,L_y,d}$ in the degree-$d$ subspace, and $m=L_x$
($L_x/2$) for $\Lambda=sq, tri (hc)$, respectively. An analogous formula is
given for Klein bottle strips. We exhibit a method for calculating
$T_{Z,\Lambda,L_y,d}$ for arbitrary $L_y$. In particular, we find some very
simple formulas for the determinant $det(T_{Z,\Lambda,L_y,d})$, and trace
$Tr(T_{Z,\Lambda,L_y})$. Corresponding results are given for the equivalent
Tutte polynomials for these lattice strips and illustrative examples are
included.

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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci