Proper encoding for snapshot-entropy scaling in two-dimensional classical spin models

We reexamine the snapshot entropy of the Ising and three-states Potts models on the L x L square lattice. Focusing on howto encode the spin snapshot, we find that the entropy at T-c scales asymptotically as S similar to (1/3) 1n L that strongly reminds us of the entanglement entropy in one-dimensional quantum critical systems. This finding seems to support that the snapshot entropy after the proper encoding is related to the holographic entanglement entropy. On the other hand, the anomalous scaling S-chi similar to chi(eta) ln chi for the coarse-grained snapshot entropy holds even for the proper encoding. These features originate in the fact that the largest singular value of the snapshot matrix is regulated by the proper encoding.