  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 (TASEP) 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.

Statistical Mechanics;Probability