Disordered configurations of the Glauber model in two-dimensional networks

¹ Scientific Computing Laboratory, Center for the Study of Complex Systems, Institute of Physics Belgrade, University of Belgrade - Pregrevica 118, 11080 Belgrade, Serbia
² Faculty of Natural Sciences and Mathematics, University of Maribor - Koroška cesta 160, SI-2000 Maribor, Slovenia
³ CAMTP – Center for Applied Mathematics and Theoretical Physics, University of Maribor - Mladinska 3, SI-2000 Maribor, Slovenia
⁴ Complexity Science Hub - Josefstädterstraße 39, A-1080 Vienna, Austria

Received: 31 January 2018
Accepted: 13 February 2018

Abstract

We analyze the ordering efficiency and the structure of disordered configurations for the zero-temperature Glauber model on Watts-Strogatz networks obtained by rewiring 2D regular square lattices. In the small-world regime, the dynamics fails to reach the ordered state in the thermodynamic limit. Due to the interplay of the perturbed regular topology and the energy neutral stochastic state transitions, the stationary state consists of two intertwined domains, manifested as multiclustered states on the original lattice. Moreover, for intermediate rewiring probabilities, one finds an additional source of disorder due to the low connectivity degree, which gives rise to small isolated droplets of spins. We also examine the ordering process in paradigmatic two-layer networks with heterogeneous rewiring probabilities. Comparing the cases of a multiplex network and the corresponding network with random inter-layer connectivity, we demonstrate that the character of the final state qualitatively depends on the type of inter-layer connections.