### Approximating the partition function of the ferromagnetic Potts modelApproximating the partition function of the ferromagnetic Potts model

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 Author Goldberg, Leslie Ann ♦ Jerrum, Mark Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©2012 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Approximation algorithms ♦ Potts model ♦ Tutte polynomial ♦ Computation complexity ♦ Phase transition ♦ Random cluster model ♦ Statistical physics Abstract We provide evidence that it is computationally difficult to approximate the partition function of the ferromagnetic $\textit{q}-state$ Potts model when $\textit{q}$ > 2. Specifically, we show that the partition function is hard for the complexity class #RHPi under approximation-preserving reducibility. Thus, it is as hard to approximate the partition function as it is to find approximate solutions to a wide range of counting problems, including that of determining the number of independent sets in a bipartite graph. Our proof exploits the first-order phase transition of the “random cluster” model, which is a probability distribution on graphs that is closely related to the $\textit{q}-state$ Potts model. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 2012-11-05 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 59 Issue Number 5 Page Count 31 Starting Page 1 Ending Page 31

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Source: ACM Digital Library