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
  Cyclic and Mobius 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 cyclic and M\"obius 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. For the cyclic case we express the
partition function as $Z(\Lambda,L_y \times L_x,q,v)=\sum_{d=0}^{L_y} c^{(d)}
Tr[(T_{Z,\Lambda,L_y,d})^m]$, where $\Lambda$ denotes lattice type, $c^{(d)}$
are specified polynomials of degree $d$ in $q$, $T_{Z,\Lambda,L_y,d}$ is the
transfer matrix in the degree-$d$ subspace, and $m=L_x$ ($L_x/2$) for
$\Lambda=sq, tri (hc)$, respectively. An analogous formula is given for
M\"obius strips. We exhibit a method for calculating $T_{Z,\Lambda,L_y,d}$ for
arbitrary $L_y$. Explicit results for arbitrary $L_y$ are given for
$T_{Z,\Lambda,L_y,d}$ with $d=L_y$ and $d=L_y-1$. In particular, we find very
simple formulas 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. We also present formulas for self-dual cyclic strips of the square
lattice.

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The categories of this paper are: math
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: supr-con