On the phase transition in the sublattice TASEP with stochastic blockage

We revisit the defect-induced nonequilibrium phase transition from a largely homogeneous free-flow phase to a phase-separated congested phase in the sublattice totally asymmetric simple exclusion process with local deterministic bulk dynamics and a stochastic defect that mimicks a random blockage. Exact results are obtained for the compressibility and density correlations for a stationary grandcanonical ensemble given by the matrix product ansatz. At the critical density the static compressibility diverges while in the phase separated state above the critical point the compressibility vanishes due to strong non-local correlations. These correlations arise from a long range effective interaction between particles that appears in the stationary state despite the locality of the microscopic dynamics.