Computational Transition at the Uniqueness Threshold

@article{Sly2010ComputationalTA,
  title={Computational Transition at the Uniqueness Threshold},
  author={Allan Sly},
  journal={2010 IEEE 51st Annual Symposium on Foundations of Computer Science},
  year={2010},
  pages={287-296}
}
  • Allan Sly
  • Published 30 May 2010
  • Mathematics, Computer Science
  • 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
The hardcore model is a model of lattice gas systems which has received much attention in statistical physics, probability theory and theoretical computer science. It is the probability distribution over independent sets $I$ of a graph weighted proportionally to $\lambda^{|I|}$ with fugacity parameter $\lambda$. We prove that at the uniqueness threshold of the hardcore model on the $d$-regular tree, approximating the partition function becomes computationally hard on graphs of maximum degree $d… 
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