Eur. Phys. J. B (2017) 90: 213
https://doi.org/10.1140/epjb/e2017-80365-3

Regular Article

“Islands in Sea” and “Lakes in Mainland” phases and related transitions simulated on a square lattice

¹ Physics Department, Charuchandra College, Kolkata 700029, India
² Physics Department, St. Xavier’s College, Kolkata 700016, India
³ Condensed Matter Physics Research Centre, Physics Department, Jadavpur University, Kolkata 700032, India

^a e-mail: sujata_tarafdar@hotmail.com

Received: 21 June 2017
Received in final form: 9 September 2017
Published online: 7 November 2017

Abstract

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.