# Surface energy and boundary layers for a chain of atoms at low temperature

## TL;DR

This paper investigates the low-temperature behavior of a chain of atoms with Lennard-Jones interactions, focusing on surface energy, boundary layers, and large deviations of Gibbs measures, revealing zero-temperature limits and correlation decay bounds.

## Contribution

It establishes large deviation principles for Gibbs measures at low temperature, characterizes surface energy functionals, and links zero-temperature limits to boundary layers and free energy corrections.

## Key findings

- Gibbs measures satisfy large deviations principles with specific energy functionals.
- Surface correction converges to zero-temperature surface energy.
- Bulk measures can be approximated by Gaussian measures.

## Abstract

We analyze the surface energy and boundary layers for a chain of atoms at low temperature for an interaction potential of Lennard-Jones type. The pressure (stress) is assumed small but positive and bounded away from zero, while the temperature $\beta^{-1}$ goes to zero. Our main results are: (1) As $\beta \to \infty$ at fixed positive pressure $p>0$, the Gibbs measures $\mu_\beta$ and $\nu_\beta$ for infinite chains and semi-infinite chains satisfy path large deviations principles. The rate functions are bulk and surface energy functionals $\overline{\mathcal{E}}_{\mathrm{bulk}}$ and $\overline{\mathcal{E}}_\mathrm{surf}$. The minimizer of the surface functional corresponds to zero temperature boundary layers. (2) The surface correction to the Gibbs free energy converges to the zero temperature surface energy, characterized with the help of the minimum of $\overline{\mathcal{E}}_\mathrm{surf}$. (3) The bulk Gibbs measure and Gibbs free energy can be approximated by their Gaussian counterparts. (4) Bounds on the decay of correlations are provided, some of them uniform in $\beta$.