Approximation of crystalline defects at finite temperature

The present paper develops an approximation framework and corresponding results for crystalline defects of a lattice at finite temperature. In a one-dimensional setting, we introduce Gibbs distributions corresponding to such defects and rigorously establish their asymptotic expansion with respect to temperature uniformly in the system size. We then give an example of using such asymptotic expansion to compare the accuracy of computations using free boundary conditions versus using an atomistic-to-continuum coupling method. For the sake of brevity, the example is limited to a defect-free crystal. We leave application of our framework to existing schemes of modeling defects for future publications.