  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 $E_l\sim l^{\Theta}$ with
$\Theta\sim 1.33(5)$. Simulations suggest that in another model of this class,
namely the four-spin model, energy is concentrated mainly in linear defects
making also in this case domain walls tensionless. Two-dimensinal variants of
these models are trivial and energy of excitations scales with the exponent
$\Theta=1.05(5)$.
