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arXiv · 2407.02603

Heider balance on Archimedean lattices and cliques

Krzysztof Malarz·Maciej Wołoszyn·Krzysztof Kułakowski
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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 $T>0$.

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Krzysztof Malarz, Maciej Wołoszyn, Krzysztof Kułakowski. 2024-07-02. Heider balance on Archimedean lattices and cliques. https://doi.org/10.1103/physreve.111.014310

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