eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2016-02-16
51:1
51:14
10.4230/LIPIcs.STACS.2016.51
article
FPTAS for Hardcore and Ising Models on Hypergraphs
Lu, Pinyan
Yang, Kuan
Zhang, Chihao
Hardcore and Ising models are two most important families of two state spin systems in statistic physics. Partition function of spin systems is the center concept in statistic physics which connects microscopic particles and their interactions with their macroscopic and statistical properties of materials such as energy, entropy, ferromagnetism, etc. If each local interaction of the system involves only two particles, the system can be described by a graph. In this case, fully polynomial-time approximation scheme (FPTAS) for computing the partition function of both hardcore and anti-ferromagnetic Ising model was designed up to the uniqueness condition of the system. These result are the best possible since approximately computing the partition function beyond this threshold is NP-hard. In this paper, we generalize these results to general physics systems, where each local interaction may involves multiple particles. Such systems are described by hypergraphs. For hardcore model, we also provide FPTAS up to the uniqueness condition, and for anti-ferromagnetic Ising model, we obtain FPTAS under a slightly stronger condition.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol047-stacs2016/LIPIcs.STACS.2016.51/LIPIcs.STACS.2016.51.pdf
hard-core model
ising model
hypergraph
spatial mixing
correlation decay