Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computing bounds for entropy of stationary Z^d Markov random fields   For any stationary $\mZ^d$-Gibbs measure that satisfies strong spatial
mixing, we obtain sequences of upper and lower approximations that converge to
its entropy. In the case, $d=2$, these approximations are efficient in the
sense that the approximations are accurate to within $\epsilon$ and can be
computed in time polynomial in $1/\epsilon$.

3
The categories of this paper are: physics
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph