  The nature of the glass transition is theoretically understood in the
mean-field limit of infinite spatial dimensions, but the problem remains
totally open in physical dimensions. Nontrivial finite-dimensional fluctuations
are hard to control analytically, and experiments fail to provide conclusive
evidence regarding the nature of the glass transition. Here, we use Monte Carlo
simulations that fully bypass the glassy slowdown, and access equilibrium
states in two-dimensional glass-forming liquids at low enough temperatures to
directly probe the transition. We find that the liquid state terminates at a
thermodynamic glass transition at zero temperature, which is associated with an
entropy crisis and a diverging static correlation length.
