Anomalous Mean-Field Criticality in Information-Driven Adaptive Networks

We study a co-evolving network model in which topology and node-level information mutually influence each other through a copying mechanism with information decay. Each node carries a binary information string that undergoes stochastic bit-flip mutations, and edge formation is conditioned on information similarity, creating a feedback loop between structure and state. The system exhibits a rich three-phase structure controlled by the dimensionless parameter θ = β/p: (i) an assortative phase (θ < θc1) with positive excess overlap q > 0, (ii) a disassortative phase (θc1 < θ < θc2) with negative excess overlap q < 0, and (iii) a random phase (θ > θc2) with vanishing correlations. Finite-size scaling analysis reveals two genuine phase transitions with critical points θc1(∞) = 1.028 ± 0.002 and θc2(∞) = 1.994 ± 0.001. Both transitions exhibit mean-field correlation length exponents ν1 ≈ ν2 ≈ 2, but distinct finite-size drift exponents b1 ≈ 0.47 and b2 ≈ 0.72, indicating different critical mechanisms within a single model. We discover that the order parameter exhibits anomalous amplitude scaling q ∼ Nβ with β ≈ −1/2, which is non-trivial and cannot be explained by statistical fluctuations alone. The disassortative phase demonstrates strengthening anti-correlations with system size, a phenomenon we term “information-induced anti-order.” The decoupling of correlation length scaling from finite-size drift represents a novel universality class in adaptive networks.