We study the BS model, which is a one-dimensional lattice field theory taking real values. Its dynamics is governed by coupled differential equations plus random nearest neighbor exchanges. The BS model has exactly two locally conserved fields. Throu
gh numerical simulations the peak structure of the steady state space-time correlations is determined and compared with nonlinear fluctuating hydrodynamics, which predicts a traveling peak with KPZ scaling function and a standing peak with a scaling function given by the completely asymmetric Levy distribution with parameter $alpha = 5/3$. As a by-product, we completely classify the universality classes for two coupled stochastic Burgers equations with arbitrary coupling coefficients.
We consider gradient fields $(phi_x:xin mathbb{Z}^d)$ whose law takes the Gibbs--Boltzmann form $Z^{-1}exp{-sum_{< x,y>}V(phi_y-phi_x)}$, where the sum runs over nearest neighbors. We assume that the potential $V$ admits the representation [V(eta):=-
logintvarrho({d}kappa)expbiggl[-{1/2}kappaet a^2biggr],] where $varrho$ is a positive measure with compact support in $(0,infty)$. Hence, the potential $V$ is symmetric, but nonconvex in general. While for strictly convex $V$s, the translation-invariant, ergodic gradient Gibbs measures are completely characterized by their tilt, a nonconvex potential as above may lead to several ergodic gradient Gibbs measures with zero tilt. Still, every ergodic, zero-tilt gradient Gibbs measure for the potential $V$ above scales to a Gaussian free field.
