Random field Ising chains with synchronous dynamics

We present an exact solution of the one-dimensional random field Ising mode l (RFIM) with synchronous rather than sequential spin-dynamics, whose equil ibrium state is characterized by a temperature-dependent pseudo-Hamiltonian , based upon a suitable adaptation of the techniques originally developed f or the sequential (Glauber) dynamics RFIM. Although deriving the solution i s somewhat more involved in the present model than in the case of the seque ntial RFIM, we are able to prove rigorously that the physics of the two RFI M versions are asymptotically identical. We thus recover the familiar devil 's staircase form for the integrated density of local magnetizations, and f ind a non-zero ground state entropy with an infinite number of singularitie s as a function of the random field strength.