arXiv:2609.38327v2 Announce Type: replace Abstract: Nontrivial dynamics can emerge in large language model (LLM)-based multi-agent systems, and preliminary evidence exists that formalisms from statistical mechanics can be effective at modeling and predicting such behaviors. In parallel, designing multi-agent communication topology for optimal task-solving is an active research question. In this paper, we focus on predicting the success of multi-agent search tasks using the formalism of absorbing state phase transitions. We first taxonomize search tasks into four types, informed by classical results in combinatorial search. We then theoretically derive a critical communication degree $d_c$, the minimum number of agents each agent can communicate with, above which incorrect hypotheses do not proliferate uncontrollably and the search enters the solved state. Finally, we evaluate frontier LLM-based multi-agent systems on real-world search and discovery tasks, software configuration debugging and physical mechanism discovery, and find that agreement with theory is mixed. LLM agents may not communicate with their neighbors and can develop strategies that are individually beneficial but limits the benefits of collaboration.