Surface energy and boundary layers for a chain of atoms at low temperature. (English) Zbl 1456.82666
Summary: 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 to be small but positive and bounded away from zero, while the temperature \(\beta^{-1}\) goes to zero. Our main results are: (1) As \(\beta \rightarrow \infty\) 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 \(\overline{\mathcal{E}}_\text{bulk}\) and \(\overline{\mathcal{E}}_\text{surf}\). 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 \(\overline{\mathcal{E}}_\text{surf}\); (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 \(\beta\).
MSC:
| 82C22 | Interacting particle systems in time-dependent statistical mechanics |
| 82C20 | Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics |
| 81V45 | Atomic physics |
| 60F10 | Large deviations |
| 74A25 | Molecular, statistical, and kinetic theories in solid mechanics |
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