Transverse Temperature Interfaces in the Katz-Lebowitz-Spohn Driven Lattice Gas

We explore the intriguing spatial patterns that emerge in a two-temperature Katz-Lebowitz-Spohn (KLS) model in two dimensions, a driven lattice gas with attractive nearest-neighbor interactions and periodic boundary conditions. The domain is split into two regions with hopping rates governed by different temperatures T > Tc and Tc, respectively, where Tc indicates the critical temperature for phase ordering, and with the temperature boundaries oriented transverse to the drive. In the hotter region, the system behaves like the (totally) asymmetric exclusion processes (T)ASEP, and experiences particle blockage in front of the interface to the critical region. We argue that transport in the subsystem is impeded by the lower current in the cooler region, which tends to set the global stationary particle current value. We observe the density profiles in both high-and low-temperature subsystems to be strikingly similar to the well-characterized coexistence and maximal-current phases in (T)ASEP models with open boundary conditions. If the lower temperature is set equal to Tc, we instead detect the corresponding critical power law density decay.