| Abstract [eng] |
This thesis investigates the influence of different delayed-interaction mechanisms on the statistical properties of ordering processes in elementary spin systems. In sociophysics, elementary spin systems, often modeled using the voter model, are used to understand and describe the formation of public opinion. The main goal of this work is to study how different delay mechanisms affect consensus formation dynamics, mean ordering times, and exit-state probabilities. The investigated models include the latent voter model proposed by Lambiotte et al. and its reversed version, as well as the polling-delay-based voter model and its version without information delay. Monte Carlo simulations were performed for fully connected systems, meaning that every particle could interact with every other particle. Particular attention was given to the influence of parameters controlling the delay duration, including copying probability, flexibility recovery probability, and polling period. The performed simulations and analysis showed that latent-state and polling mechanisms can significantly modify the statistical properties of ordering in elementary spin systems compared with the classical voter model. In the Lambiotte et al. latent voter model, temporary agent inflexibility reduces the importance of the initial condition. When the initial state is not strongly polarized, increasing the delay duration causes the probabilities of reaching the two ordered states to become approximately equal. In contrast, the polling-delay mechanism strengthens the influence of initial polarization and increases the probability of reaching the corresponding ordered state. The influence of model parameters was also analyzed. Increasing the copying probability in the latent voter model increases the ordering time because a large number of inflexible particles forms rapidly. In all investigated models, increasing the delay duration, either by decreasing the flexibility recovery probability in the latent voter model or by increasing the polling period in the polling-based model, leads to stronger deviations from the statistical properties of the classical voter model. The results demonstrate that different delay mechanisms can produce qualitatively different ordering behavior in elementary interacting spin systems. |
