2025/04/05 by Roy, Dipankar, Dhar, Abhishek, Kulkarni, Manas +1 · 1 citation
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2504.04162
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 = \tfrac32. 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 XY ≥ 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).