A new scenario describing `water-like` thermodynamic anomalies - the double liquid-liquid critical point scenario*

Thermodynamic `water-like' anomalies in liquids have been a long unsolved problem in terms of
origin and implications for nature of the liquid (and other similar states). The widely accepted thermodynamic scenario that describes this behaviour in water models and Stillinger-Weber (SW) potential silicon is the second (liquid-liquid) critical point (LLCP) scenario. In this work we present simulation evidence for a novel scenario in wide range of SW liquids. In this scenario the locus of liquid density anomalies (the density minimum and maximum) encloses a region of thermodynamic space with two liquid-liquid critical points connected by a first order transition. We scan the parameter space of the SW potential (tetrahedrality and ideal bond angle parameter) and observe limiting instances where density anomalies disappear. We observe the interactions of density anomaly with the compressibility anomaly, heat capacity anomaly and spinodal line and confirm they show thermodynamically consistent behaviour.