Forma, Vol. 15 (No. 4), pp. 415-428, 2000
Original Paper

Phase Transitions of Route Patterns in the Steiner's Problem with Four Cities

Yoshihiro Yamaguchi

Teikyo Heisei University, Ichihara, Chiba 290-0193, Japan

(Received December 6, 1999; Accepted April 3, 2000)

Keywords: Steiner's Problem, Phase Transition

Abstract. The route patterns of the simplified Steiner's problem with four cities are investigated by the experiment using soap film and by numerical calculation. We show that the change of route patterns are understandable by the concept of phase transition of thermodynamics. The change of patterns is categorized into two cases. The first one shows the first order phase transition and the other shows the second order phase transition. The third order phase transition occurs if the particular path in phase plane is chosen.

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