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×L square lattice. Focusing on how to encode the spin snapshot, we find that the entropy at Tc scales asymptotically as S∼(1/3)lnL 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 Sχ∼χηlnχ 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.