"Burning and sticking" model for a porous material: suppression of the topological phase transition due to the backbone reinforcement effect

We introduce and study the “burning-and-sticking” (BS) lattice model for the porous material that involves sticking of emerging finite clusters to the mainland. In contrast with other single-cluster models, it does not demonstrate any phase transition: the backbone exists at arbitrarily low concentrations. The same is true for hybrid models, where the sticking events occur with probability $q$: the backbone survives at arbitrarily low $q$. Disappearance of the phase transition is attributed to the backbone reinforcement effect, generic for models with sticking. A relation between BS and the cluster-cluster aggregation is briefly discussed.