Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Truncation of Systems with Non-Summable Interactions   In this note we consider long range $q$-states Potts models on
$\mathbf{Z}^d$, $d\geq 2$. For various families of non-summable ferromagnetic
pair potentials $\phi(x)\geq 0$, we show that there exists, for all inverse
temperature $\beta>0$, an integer $N$ such that the truncated model, in which
all interactions between spins at distance larger than $N$ are suppressed, has
at least $q$ distinct infinite-volume Gibbs states. This holds, in particular,
for all potentials whose asymptotic behaviour is of the type $\phi(x)\sim
\|x\|^{-\alpha}$, $0\leq\alpha\leq d$. These results are obtained using simple
percolation arguments.

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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: cs
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys