Metastability in the two-dimensional Ising Spin model subject to Glauber dynamics

Abstract

The model studied in this thesis is the two-dimensional Ising Spin model subject to Glauber dynamics in the low-temperature limit. The main objects of interest to this thesis are the transition time from the metastable state to the stable state and the critical fluctuation the needed in order to perform the transition towards the equilibrium. The main goal is to give sharp estimates on the expected hitting time of the stable configuration when the starting configuration is the metastable configuration. The expected hitting time is estimated by using potential theory which reduces the analysis to a computation of Newtonian capacities. These capacities can be estimated in terms of properties of the energy landscape generated by the associated Hamiltonian in the limit of zero temperature.