Consensus and Factual Dynamics in Large Populations of Interacting Language Models

Abstract

Large Language Model (LLM) agents are increasingly deployed as populations of interacting entities, in which consensus --agreement on a shared answer-- emerges as a collective, unengineered behaviour. Prior work on LLM consensus shows that agents can cross-verify their answers and converge towards more factual responses, treating agreement as a proxy for correctness. However, these studies usually fix a single interaction structure, leaving open how consensus depends on how agents interact. We address this gap by introducing RHEON, a physics-inspired framework that recasts a population drawn from a single frozen model as an evolving $O(n)$ spin system on a ladder of interaction geometries of increasing effective dimension --from a 1D ring to a full-coupling mean-field graph-- with the sampling temperature $T$ as the tunable source of thermal disorder, evolved through a Glauber-like asynchronous dynamics. Sweeping RHEON across $432$ configurations of prompt, population size, communication topology, and sampling temperature yields Eraclitus-4.7M, a tagged evolutionary corpus of $4.7$ million responses. We find that agents reach their strongest consensus gain within the first few update sweeps and that increasing the number of neighbours per agent accelerates convergence on average. We further show that whether a configuration settles on factually correct or hallucinated consensus is not predictable from its initial state alone, and that the hallucination-minimising temperature depends on how the agents are coupled, so the common near-greedy default is not automatically the safest. Finally, semantic agreement correlates positively with factual convergence, and interaction strengthens the association, yet never enough for unanimity to certify correctness.