Journal of the European Mathematical Society

We considerably improve upon the recent result of Martinelli and Toninelli on\nthe mixing time of Glauber dynamics for the 2D Ising model in a box of side $L$\nat low temperature and with random boundary conditions whose distribution $P$\nstochastically dominates the extremal plus phase. An important special case is\nwhen $P$ is concentrated on the homogeneous all-plus configuration, where the\nmixing time $T_{mix}$ is conjectured to be polynomial in $L$. In [MT] it was\nshown that for a large enough inverse-temperature $\\beta$ and any $\\epsilon >0$\nthere exists $c=c(\\beta,\\epsilon)$ such that $\\lim_{L\\to\\infty}P(T_{mix}\\geq\n\\exp({c L^\\epsilon}))=0$. In particular, for the all-plus boundary…