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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 | Abstract: | We 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 | Services: | Forum | Review | PDF | Favorites |
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