Approximating the partition function of the ferromagnetic Potts model
Abstract
We provide evidence that it is computationally difficult to approximate the partition function of the ferromagnetic q-state Potts model when q>2. Specifically we show that the partition function is hard for the complexity class #RHPi_1 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 q-state Potts model.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2010
- DOI:
- 10.48550/arXiv.1002.0986
- arXiv:
- arXiv:1002.0986
- Bibcode:
- 2010arXiv1002.0986G
- Keywords:
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- Computer Science - Computational Complexity;
- Mathematics - Combinatorics;
- F.2.2;
- F.1.3;
- G.2.2
- E-Print:
- Minor corrections