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A two-dimensional model of interacting plaquettes is studied by means of thereal space renormalization group approach. Interactions between the plaquettesare mediated solely by spin excitations on the plaquettes. Depending on theplaquette-plaquette coupling $J$, we find two regimes:  "confinement" $J_c< J\leq 1$, where the singlet ground state forms aninfinite ("confined") cluster in the thermodynamical limit. Here thesinglet-triplet gap vanishes, which is the signature for long range spin-spincorrelators.  "deconfinement" $0\leq J< J_c$, where the singlet ground state "deconfines" -i.e. factorizes - into finite $n$-clusters of size $2^n\times 2^n$, with $n\leqn_c(J)$. Here the singlet-triplet gap is finite.  The critical value turns out to be $J_c=0.473528..$.

Deconfinement phase transition in a two-dimensional model of interacting $2\times 2$ plaquettes