Kosterlitz-Thouless Transition of the XY model on rewired square lattices

The ferromagnetic XY model (O(2) symmetry) on decorated square lattices is\ud studied via Monte Carlo simulation to probe the role played by an increase in coordination\ud number on the existing Kosterlitz-Thouless (KT) transition [1]. It is a unique transition between\ud the quasi-long range order (QLRO), also called the KT phase, and the paramagnetic phase at\ud higher temperature [2, 3]. The QLRO is the only type of order allowed by theMermin-Hohenberg\ud theorem for two dimensional (2D) spin model with continuous symmetry [4]. In diluted square\ud lattices, where some links are depleted, it was found that the KT phase remains so long as the\ud links are percolated. Here we probe whether the increase in average number of links preserves\ud or destroys the KT phase. The decorated lattice is obtained by adding an extra link to each site\ud of a square lattice, randomly connecting each site to one of its next-nearest neighbors [5]. The\ud average number of nearest links increases from two to three, which corresponds to an increase\ud in dimensionality. The existence of KT phase is characterized by the correlation ratio, which\ud was also used in characterizing the critical properties of the 2D edge-cubic model [6]. It was\ud found that the KT phase shifted to higher temperature, which indicates that the KT phase on\ud decorated lattices is more robust against thermal fluctuation compared to that of the native\ud square lattice. [3].\ud Reference