期刊
PROBABILITY THEORY AND RELATED FIELDS
卷 176, 期 3-4, 页码 851-895出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s00440-019-00928-y
关键词
Approximate sampling; Approximation algorithms; FPTAS; Discrete spin systems; Pirogov-Sinai theory; Cluster expansion
资金
- EPSRC [EP/P009913/1, EP/P003656/1]
- NSF [DMS-1847451]
- NWO Veni Grant
- EPSRC [EP/P003656/1, EP/P009913/1] Funding Source: UKRI
We develop an efficient algorithmic approach for approximate counting and sampling in the low-temperature regime of a broad class of statistical physics models on finite subsets of the lattice Zd and on the torus (Z/nZ)d. Our approach is based on combining contour representations from Pirogov-Sinai theory with Barvinok's approach to approximate counting using truncated Taylor series. Some consequences of our main results include an FPTAS for approximating the partition function of the hard-core model at sufficiently high fugacity on subsets of Zd with appropriate boundary conditions and an efficient sampling algorithm for the ferromagnetic Potts model on the discrete torus (Z/nZ)d at sufficiently low temperature.
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