The hard-core model is a basic and important model in statistical mechanics, probability, and theoretical computer science. I’ll introduce the model, and after describing some known algorithmic results, will discuss a polynomial-time algorithm for approximately sampling from the hard-core model at high densities on the integer lattices. This is the regime in which the Glauber dynamics are known to mix exponentially slowly. Our algorithm relies in an essential way on Pirogov-Sinai theory, an important tool for understanding the phase diagram of high-density discrete statistical mechanics models.
This is joint work with Will Perkins and Guus Regts.