Another look at the phenomenon of phase transition

This study is motivated by the question whether there exists a characteristic feature common to the phenomenon of phase transition of properties taking place in the course of evolution of various sets of objects of different nature. A novel measure model of phase transition is presented, providing an insight into the process underlying different phase transitions. First, it is shown to conform to several famous and extensively investigated cases of phase transition. Then a few close consequences of applying the measure model are presented. It has been proved that monotone properties undergo a sharp phase transition. The measure model provides a sufficient condition of a sharp phase transition common to monotone and non-monotone properties as well. The measure model reveals that if a property Q undergoes a phase transition in the course of evolution of objects of a certain type, then there exist other secondary properties related to the measure of Q that also undergo a phase transition during the evolution.

Keywords

• Random graphs,
• Integer partitions,
• Propositional satisfiability,
• 3-sat,
• Monotone qualitative changes