Discrete minimal surfaces: critical points of the area functional from integrable systems

We define two types of discrete minimal surfaces whose cell decompositions are arbitrary. These two types of discrete minimal surfaces are conjugate to each other and generalize earlier notions of discrete minimal surfaces: circular minimal, s-isothermic minimal and conical minimal surfaces. We show that each discrete minimal surface corresponds to a harmonic function on a planar mesh. Furthermore we show that all minimal surfaces in certain associated family, including those from discrete isothermic nets and Schramm's orthogonal circle patterns, are critical points of the area functional.