Study of phase transitions on graphs in presence of noise
Yadav, Vikas (2005) Study of phase transitions on graphs in presence of noise. Publisher UNSPECIFIED.
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In this article, the phase transition behavior emerging from the interactions among multiple agents in the presence of noise is studied and a simple discrete-time model is presented in which a group of non-mobile agents form either a fixed connected graph or a random graph process, and each agent, taking binary value either +1 or −1, updates its value according to its previous value and the noisy measurements of the connected agents’ values. Mathematical proofs for the occurrence of the following phase transition behavior are provided: At a noise level higher than some threshold, the system generates symmetric behavior; whereas at a noise level lower than the threshold, the system exhibits spontaneous symmetry breaking. The threshold is found analytically. The phase transition results hold for any dimension. This result may be found useful in the study of the collective behavior of complex systems under communication constraints.
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