Breakdown of a topological transition in two-dimensional spin-ice due to geometry effects

We investigate the topological transition that takes place in spin-ice systems when a polarising field is applied along a principal axis. In particular, we analyse a two dimensional spin-ice model; we find that the topological transition is strongly affected by geometrical constraints in the shape of the sample, and that in the case where the dimension perpendicular to the field is much smaller than the longitudinal one, i.e. in the quasi-1D spin-ice-ladder limit, it splits into a series of first-order phase transitions characterised by sharp spikes in the specific heat and susceptibility.