The Widom line in the Ising model on a decorated bilayer lattice

There has been much recent interest devoted to a class of frustrated one-dimensional statistical mechanics lattice models which exhibit sharp thermodynamics. In this work, we study an extension of one of these models to two dimensions, the Ising model on a decorated bilayer lattice. We show that the pseudo-transitions of the one-dimensional models become a real first order phase transition in this two-dimensional analogue. Moreover, the pseudo-transition behaviour is found to still exist above a bi-critical point. This can be characterised as a Widom line, which allows a reinterpretation of the physics in the previously studied one-dimensional models.