  We study the decay of the false vacuum in the scaling Ising and tricritical
Ising field theories using the Truncated Conformal Space Approach and compare
the numerical results to theoretical predictions in the thin wall limit. In the
Ising case, the results are consistent with previous studies on the quantum
spin chain and the $\varphi^4$ quantum field theory; in particular we confirm
that while the theoretical predictions get the dependence of the bubble
nucleation rate on the latent heat right, they are off by a model dependent
overall coefficient. The tricritical Ising model allows us on the other hand to
examine more exotic vacuum degeneracy structures, such as three vacua or two
asymmetric vacua, which leads us to study several novel scenarios of false
vacuum decay by lifting the vacuum degeneracy using different perturbations.
