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We prove a new lower bound on the critical density $\rho_c$ of the hard diskmodel, i.e., the density below which it is possible to efficiently samplerandom configurations of $n$ non-overlapping disks in a unit torus. We use aclassic Markov chain which moves one disk at a time, but with an improved pathcoupling analysis. Our main tool is an optimized metric on neighboring pairs ofconfigurations, i.e., configurations that differ in the position of a singledisk: we define a metric that depends on the difference in these positions, andwhich approaches zero continuously as they coincide. This improves the previouslower bound $\rho_c \ge 1/8$ to $\rho_c \ge 0.154$.

Lower Bounds on the Critical Density in the Hard Disk Model via Optimized Metrics