“Islands in Sea” and “Lakes in Mainland” phases and related transitions simulated on a square lattice
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We describe the Island-Mainland (IM) transition on a square lattice. Black squares are randomly dropped on a white background, with increasing concentration p. We define black (white) clusters as groups of black (white) squares, connected through edges or corners on a quasi-2D system. At a certain p the black islands in white sea (IS) phase crosses over to a mixed phase (MP). At still larger p the MP phase crosses over to the lakes in mainland (LM) phase with white lakes in a black mainland. We show that the Euler number, defined as difference between number of white clusters and number of black clusters goes through extrema near these transition points. The phenomenon is supported by experimental observations.
KeywordsStatistical and Nonlinear Physics
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