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29 March 2024
 
  » arxiv » 1304.4854

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Critical behaviour of the XY -rotors model on regular and small world networks
Sarah De Nigris ; Xavier Leoncini ;
Date 17 Apr 2013
AbstractWe study the XY -rotors model on small networks whose number of links scales with the system size N_{links}sim N^{gamma}, where 1legammale2 . We first focus on regular one dimensional rings. For gamma<1.5 the model behaves like short-range one and no phase transition occurs. For gamma>1.5, the system equilibrium properties are found to be identical to the mean field, which displays a second order phase transition at epsilon_{c}=0.75 . Moreover for gamma_{c}=1.5 we find that a non trivial state emerges, characterized by an infinite susceptibility. We then consider small world networks, using the Watts-Strogatz mechanism on the regular networks parametrized by gamma . We first analyze the topology and find that the small world regime appears for rewiring probabilities which scale as p_{SW}propto1/N^{gamma} . Then considering the XY -rotors model on these networks, we find that a second order phase transition occurs at a critical energy varepsilon_{c} which logarithmically depends on the topological parameters p and gamma . We also define a critical probability p_{MF}, corresponding to the probability beyond which the mean field is quantitatively recovered, and we analyze its dependence on gamma .
Source arXiv, 1304.4854
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