This seminar is thought as an introductory talk to discrete-to-continuum variational analysis. Here the general objective is to characterise the macroscopic behaviour
of energy-driven atomistic systems while keeping the scale-dependent relevant microscopic information.
This is done via Γ-convergence, which allows to coarse-grain discrete functionals to their
continuum counterparts as the discretisation parameter vanishes.
In this talk we will focus on some models with a particularly rich energy landscape, namely Ising
and spin models such as the classical XY-model. In the first part I will give a short introduction
to the topic and review some of the classical results in this context. In the second part I
will present some recent results obtained in collaboration with Marco Cicalese, Leonard Kreutz, and
Gianluca Orlando on the antiferromagnetic XY-model on the triangular lattice.
