Collective Alignment in LLM Multi-Agent Systems: Disentangling Bias from Cooperation via Statistical Physics

arXiv:2605.10528v1 Announce Type: cross Abstract: We investigate the emergent collective dynamics of LLM-based multi-agent systems on a 2D square lattice and present a model-agnostic statistical-physics method to disentangle social conformity from intrinsic bias, compute critical exponents, and probe the collective behavior and possible phase transitions of multi-agent systems. In our framework, each node of an L!imes!L lattice hosts an identical LLM agent holding a binary state (+1/-1, mapped to yes/no) and updating it by querying the model conditioned on the four nearest-neighbor states. The sampler temperature T serves as the sole control parameter. Across three open-weight models (llama3.1:8b, phi4-mini:3.8b, mistral:7b), we measure magnetization and susceptibility under a global-flip protocol designed to probe Z_2 symmetry. All models display temperature-driven order-disorder crossovers and susceptibility peaks; finite-size scaling on even-L lattices yields effective exponents gamma/nu whose values are model-dependent, close to but incompatible with the 2D Ising universality class (gamma/nu=7/4). Our method enables the extraction of effective eta-weighted couplings ilde{J}(T) and fields ilde{h}(T), which serve as a measure of social conformity and intrinsic bias. In the models we analyzed, we found that collective alignment is dominated by an intrinsic bias (ilde{h}ggilde{J}) rather than by cooperative neighbor coupling, producing field-driven crossovers instead of genuine phase transitions. These effective parameters vary qualitatively across models, providing compact collective-behavior fingerprints for LLM agents and a quantitative diagnostic for the reliability of multi-agent consensus and collective alignment.

Source: arXiv cs.CL | 2026-05-12