Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase Transitions on Fixed Connected Graphs and Random Graphs in the
  Presence of Noise   In this paper, we study the phase transition behavior emerging from the
interactions among multiple agents in the presence of noise. We propose a
simple discrete-time model in which a group of non-mobile agents form either a
fixed connected graph or a random graph process, and each agent, taking bipolar
value either +1 or -1, updates its value according to its previous value and
the noisy measurements of the values of the agents connected to it. We present
proofs for the occurrence of the following phase transition behavior: At a
noise level higher than some threshold, the system generates symmetric behavior
(vapor or melt of magnetization) or disagreement; whereas at a noise level
lower than the threshold, the system exhibits spontaneous symmetry breaking
(solid or magnetization) or consensus. The threshold is found analytically. The
phase transition occurs for any dimension. Finally, we demonstrate the phase
transition behavior and all analytic results using simulations. This result may
be found useful in the study of the collective behavior of complex systems
under communication constraints.

26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph