Fixed points and universality classes in coupled Kardar–Parisi–Zhang equations

We study coupled KPZ equations with three control parameters X , Y , T . These equations are used in the context of stretched polymers in a random medium, for the spacetime spin–spin correlator of the isotropic quantum Heisenberg chain, and for exciton–polariton condensates. In an earlier article we investigated merely the diagonal X = Y , T = 1. Then the stationary measure is delta-correlated Gaussian and the dynamical exponent is obtained numerically to be close to z = 3 2 . We observed that the scaling functions of the dynamic correlator change smoothly when varying X . In this contribution, the analysis is extended to the whole X – Y – T plane. Solutions are stable only if X Y ⩾ 0 . Based on numerical simulations, the static correlator still has rapid decay. We argue that the parameter space is foliated into distinct universality classes. They are labeled by X and consist of half-planes parallel to the Y – T plane containing the point ( X , X , 1 ) .