3-State Potts model and automorphism of vertex operator algebra of order 3

We define an automorphism of VOA of order 3 by using a sub VOA isomorphic to a direct sum of 3-state Potts models $L(\ff,0)$ and an its module $L(\ff,3)$. This automorphism is a 3A element of the monster simple group if $V$ is the moonshine VOA $V^{\natural}$.