Finite-size scaling in the steady state of the fully asymmetric exclusion process.

Finite-size scaling expressions for the current near the continuous phase transition and for the local density near the first-order transition are found in the steady state of the one-dimensional fully asymmetric simple-exclusion process with open boundaries and discrete-time dynamics. The corresponding finite-size scaling variables are identified as the ratio of the chain length to the localization length of the relevant domain wall.