Random field Ising chains with synchronous dynamics

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