Water-like thermodynamic anomalies in an analytically solvable 1D model

For something so ubiquitous and essential to human life, the water molecule is surprisingly unusual. Water molecules are highly polar, and can interact through either short-range Van de Waals interactions or by forming slightly longer-range hydrogen bonds. Collectively, they can be found in a number of phases. Uniquely among small molecules, it has a solid phase that is less dense than a liquid phase, a result that is counter-intuitive on entropic grounds alone.

For both historical and practical reasons, the thermodynamical properties of water have been extensively studied, and much is known about their peculiarities. A number of recalcitrant open questions remain, however. The so-called anomalous expansion of water referred to above, is still the subject of active research. In this and many other similar problems, simplified lattice models of reduced dimensionality can be useful

Out aim in this work is to generate the simplest possible lattice model that qualitatively captures the short-range interaction between water molecules, obtain its partition function analytically, and derive its thermodynamical properties. We show that even this toy model will, without any fine-tuning, produce distinct states/quasi-phases