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Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2025, Tutor: Oriol Artime Vila

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This work analyzes the non-equilibrium properties of the Voter Model and its noisy extensions (Noisy Voter Model and Voter Model with Global Noise). For the Voter Model on regular lattices, the known conservation of average magnetization ⟨m⟩ is confirmed, and the interface density ⟨ρ⟩ decays toward consensus following a dimension-dependent scaling. In the noisy models on all-to-all networks, the magnetization distribution from simulations matches the stationary Fokker-Planck solution. The Noisy Voter Model exhibits a bias toward m = 0.5, causing
a bimodal-to-unimodal transition as noise a increases. Global noise flattens the distribution, becoming uniform at a = 1. The average consensus time ⟨t⟩ peaks at the central value of initial magnetization. Increasing a delays consensus in the Noisy Voter Model, but accelerates it under global noise by disrupting metastable clusters. These results highlight the distinct roles of local and global noise in collective dynamics.