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In [2] it has been proved that a linear Hamiltonian lattice field perturbedby a conservative stochastic noise belongs to the 3/2-L\'evy/Diffusiveuniversality class in the nonlinear fluctuating theory terminology [15], i.e.energy superdiffuses like an asymmetric stable 3/2-L\'evy process and volumelike a Brownian motion. According to this theory this should remain valid atzero tension if the harmonic potential is replaced by an even potential. Inthis work we consider a quartic anharmonicity and show that the result obtainedin the harmonic case persists up to some small critical value of theanharmonicity.

Nonlinear Perturbation of a Noisy Hamiltonian Lattice Field Model: Universality Persistence