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First-order phase transition by the XY-model of particle dynamics

A gas-liquid type of phase transition is found based on the particle dynamics on a radius-R circle in which the coordinate appears as the angle-variable of the 1D XY-model. Due to the specific appearance of a compact-space radius (volume) in the present interpretation of the XY-model, the ground state develops a minimum at some critical radius, leading to the multi-valued Gibbs energy similar to systems with first-order phase transition.