Heider balance on Archimedean lattices and cliques.

Abstract

We investigate the work function U(T) for the Heider balance, driven by a thermal noise T, on several planar networks that contain separated triangles, pairs of triangles, chains of triangles, and complex structures of triangles. In simulations, the heat-bath algorithm is applied. Two schemes of link values updating are considered: synchronous and asynchronous (sequential). The latter results are compared with analytical calculations for small cliques. We argue that the actual shape of U(T) is a consequence of a local topology rather than of a macroscopic ordering. Finally, we present the mathematical proof that for any planar lattice, perfect structural (Heider) balance is unreachable at T>0.