Stretched exponentials and tensionless glass in the plaquette Ising model

Using Monte Carlo simulations, we show that the autocorrelation function C(t) in the d = 3 Ising model with a plaquette interaction has a stretched-exponential decay in a supercooled liquid phase. Such a decay characterizes also some ground-state probability distributions obtained from the numerically exact counting of up to 10(450) configurations. A related model with a strongly degenerate ground state but lacking glassy features does not exhibit such a decay. Although the stretched exponential decay of C(t) in the three-dimensional supercooled liquid is inconsistent with the droplet model, its modification that considers tensionless droplets might explain such a decay. An indication that tensionless droplets might play some role comes from the analysis of low-temperature domains that compose the glassy state. It shows that the energy of a domain of size l scales as l(1.15), hence these domains are indeed tensionless.