In this thesis we present a thorough study of the static and dynamic properties of the 2D sixteen-vertex model or, in other words, a simplified version of the dipolar spin-ice model. After a general discussion on frustrated magnets, and spin-ice in particular, we motivate the introduction of our model in order to study the collective behaviour of spin-ice. We use a rejection-free continuous-time Monte Carlo algorithm with local spin-flip updates to analyse the equilibrium phases and the critical properties of the 2D model. We compare our results with the integrable cases. We extend the model to be defined on carefully chosen trees and employ a Bethe-Peierls approximation to study its equilibrium properties. The range of validity of the approximation is discussed by comparing the results obtained analytically for the model defined on trees with the exact and numerical results obtained for the 2D model. Motivated by advent of artificial spin-ice realisations, we set the parameters of the model in order to reproduce the experimental situation. We show that the sixteen-vertex model gives an accurate description of the thermodynamics of artificial spin-ice samples. Our theoretical results are in quasi-quantitative agreement with experimental data obtained in as-grown samples away from the expected critical point. The phase diagram of the sixteen-vertex model and the nature of the equilibrium phases is presented in detail. Our model is build as a stochastic extension of the integrable six-vertex model in order to in- clude thermal fluctuations in the form of defects. We study the ordering dynamics of the system following different kind of quenches by means of Monte Carlo simulations. We analysed the evo- lution of the density of defects and we identified the dynamical mechanisms leading the different ordering processes. We showed that the dynamics proceed through coarsening accordingly to the dynamical scaling picture. The interplay between localised and extended topological defects is discussed. We study in detail the existence of a dynamical arrest following a quench as observed in 3D dipolar spin-ice.
