Paper Info
Title
Stratified sampling for the Ising model: A graph-theoretic approach.
Abstract
We present a new approach to a classical problem in statistical physics: estimating the partition function and thermodynamic quantities of the ferromagnetic Ising model. The standard approach to this problem is to use Markov chain Monte Carlo methods that are based on the classic work of Metropolis et al. (1953). Although great improvements to these original ideas have been made, there remains scope for improvement. The first polynomial time algorithm for the estimation of the partition function was developed by Jerrum and Sinclair (1993), who reduced the problem to counting subgraphs via the high-temperature expansion. However, the polynomial bound achieved has large degree and so yields an algorithm that is too slow for practical use. Our approach, which also uses the high-temperature expansion, yields a broad class of Monte Carlo algorithms that are not based on the work of Metropolis et al., but instead use heuristic sampling techniques. In particular, we estimate coefficients of a polynomial that, once obtained, can be used to determine the quantities of interest at all temperatures simultaneously. This class of algorithms can be applied to any underlying graph, with or without an external field. These algorithms are also highly parallelizable, which, among other features, makes their implementation possible in practice.
Year
DOI
Venue
2015
10.1016/j.cpc.2015.01.005
Computer Physics Communications
Keywords
Field
DocType
Ising model,Partition function,Graph theory,Heuristic sampling,High-temperature expansion
Graph theory,Discrete mathematics,Graph,Partition function (statistical mechanics),NIST,Ising model,Stratified sampling,Mathematics
Journal
Volume
ISSN
Citations 
191
0010-4655
0
PageRank 
References 
Authors
0.34
4
4
Name
Order
Citations
PageRank
Amanda Pascoe Streib174.10
Noah Streib200.34
Beichl, Isabel36322.58
Francis Sullivan44917.33