Accurate lower bounds on 2-D constraint capacities from corner transfer matrices

Abstract

We analyse the capacity of several 2-D constraint families - the exclusion, coloring, parity, and charge model families. Using Baxter's corner transfer matrix formalism combined with the corner transfer matrix renormalization group method of Nishino and Okunishi, we calculate very tight lower bounds and estimates on the growth rates of these models. Our results strongly improve previous known lower bounds and lead to the surprising conjecture that the capacity of the even and charge(3) constraints are identical. © 2014 IEEE.