Emergence of a non trivial fluctuating phase in the XY model on regular networks
We study an XY-rotor model on regular one dimensional lattices by varying the number of neighbours. The parameter $2\geγ\ge1$ is defined. $γ=2$ corresponds to mean field and $γ=1$ to nearest neighbours coupling. We find that for $γ<1.5$ the system does not exhibit a phase transition, while for $γ> 1.5$ the mean field second order transition is recovered. For the critical value $γ=γ_c=1.5$, the systems can be in a non trivial fluctuating phase for whichthe magnetisation shows important fluctuations in a given temperature range, implying an infinite susceptibility. For all values of $γ$ the magnetisation is computed analytically in the low temperatures range and the magnetised versus non-magnetised state which depends on the value of $γ$ is recovered, confirming the critical value $γ_{c}=1.5$.