Tensionless structure of a glassy phase

We study a class of homogeneous finite-dimensional Ising models which were recently shown to exhibit glassy properties. Monte Carlo simulations of a particular three-dimensional model in this class show that the glassy phase obtained under slow cooling is dominated by large-scale excitations whose energy E(l) scales with their size l as E(l) approximately l(Theta) with Theta approximately 1.33(20). Simulations suggest that in another model of this class, namely the four-spin model, energy is concentrated mainly in linear defects, making the domain walls tensionless in this case also. Two-dimensional variants of these models are trivial and most likely the energy of excitations scales with the exponent Theta=1.