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

## TL;DR

This paper investigates how a nonlinear perturbation affects the universality class of a noisy Hamiltonian lattice field model, showing that superdiffusive behavior persists under small anharmonicity.

## Contribution

It extends previous linear models to include quartic anharmonicity, demonstrating the persistence of universality results in the nonlinear regime.

## Key findings

- Superdiffusive energy transport persists with small anharmonicity.
- Universality class remains unchanged up to a critical anharmonicity.
- Results support the robustness of nonlinear fluctuating theory predictions.

## Abstract

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