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We analyse the capacity of several two-dimensional constraint families - theexclusion, colouring, parity and charge model families. Using Baxter's cornertransfer matrix formalism combined with the corner transfer matrixrenormalisation group method of Nishino and Okunishi, we calculate very tightlower bounds and estimates on the growth rate of these models. Our resultsstrongly improve previous known lower bounds, and lead to the surprisingconjecture that the capacity of the even and charge(3) constraints areidentical.

Accurate lower bounds on two-dimensional constraint capacities from corner transfer matrices