Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient sampling and counting algorithms for the Potts model on
  $\mathbb Z^d$ at all temperatures   For $d \ge 2$ and all $q\geq q_{0}(d)$ we give an efficient algorithm to
approximately sample from the $q$-state ferromagnetic Potts and random cluster
models on the torus $(\mathbb Z / n \mathbb Z )^d$ for any inverse temperature
$\beta\geq 0$. This stands in contrast to Markov chain mixing time results: the
Glauber dynamics mix slowly at and below the critical temperature, and the
Swendsen--Wang dynamics mix slowly at the critical temperature. We also provide
an efficient algorithm (an FPRAS) for approximating the partition functions of
these models.
  Our algorithms are based on representing the random cluster model as a
contour model using Pirogov-Sinai theory, and then computing an accurate
approximation of the logarithm of the partition function by inductively
truncating the resulting cluster expansion. The main innovation of our approach
is an algorithmic treatment of unstable ground states; this is essential for
our algorithms to apply to all inverse temperatures $\beta$. By treating
unstable ground states our work gives a general template for converting
probabilistic applications of Pirogov--Sinai theory to efficient algorithms.

28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat