Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: No phase transition for Gaussian fields with bounded spins   Let a<b, \Omega=[a,b]^{\Z^d} and H be the (formal) Hamiltonian defined on
\Omega by
  H(\eta) = \frac12 \sum_{x,y\in\Z^d} J(x-y) (\eta(x)-\eta(y))^2 where
J:\Z^d\to\R is any summable non-negative symmetric function (J(x)\ge 0 for all
x\in\Z^d, \sum_x J(x)<\infty and J(x)=J(-x)). We prove that there is a unique
Gibbs measure on \Omega associated to H. The result is a consequence of the
fact that the corresponding Gibbs sampler is attractive and has a unique
invariant measure.

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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: eess
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
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The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci