Correlation Decay and Partition Function Zeros: Algorithms and Phase Transitions

@article{Liu2019CorrelationDA,
  title={Correlation Decay and Partition Function Zeros: Algorithms and Phase Transitions},
  author={Jingcheng Liu and Alistair Sinclair and Piyush Srivastava},
  journal={SIAM Journal on Computing},
  year={2019}
}
We explore connections between the phenomenon of correlation decay and the location of Lee-Yang and Fisher zeros for various spin systems. In particular we show that, in many instances, proofs showing that weak spatial mixing on the Bethe lattice (infinite $\Delta$-regular tree) implies strong spatial mixing on all graphs of maximum degree $\Delta$ can be lifted to the complex plane, establishing the absence of zeros of the associated partition function in a complex neighborhood of the region… 

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