FPTAS for Hardcore and Ising Models on Hypergraphs
Abstract
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 polynomialtime approximation scheme (FPTAS) for computing the partition function of both hardcore and antiferromagnetic 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 NPhard. 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 antiferromagnetic Ising model, we obtain FPTAS where a slightly stronger condition holds.
 Publication:

arXiv eprints
 Pub Date:
 September 2015
 arXiv:
 arXiv:1509.05494
 Bibcode:
 2015arXiv150905494L
 Keywords:

 Computer Science  Data Structures and Algorithms