Phase transition in the two-dimensional classical XY model

J. K. Kim

Petter Minnhagen, Beom Jun Kim, Petter Holme

Johannes E. Van Himbergen

A systematic numerical study of the relevant finite-size effects of the helicity modulus for the two-dimensional classical XY model demonstrates the usefulness of this quantity as a means of obtaining information about Kosterlitz-Thouless type phase transitions. In this way, one does not have to compute correlation functions on finite lattices, and fit or compare the data thus obtained to theoretical scaling predictions, which only pertain to extremely large lattices. The approach may have many applications to systems of current interest that exhibit XY-like phase transitions.

Anderson Barbosa Lima, B. V. Costa

Using Monte Carlo simulations we have investigated the critical behavior of the classical fully frustrated XY model in two dimensions in a square lattice. There are two phase transitions in the model, one of the Berezinskii-Kosterlitz-Thouless type and a Z2 transition at higher temperature. We show that the vortex anti-vortex density has a clear signature of the Z2 phase transition at exactly the percolation threshold.

Hassan Chamati, Silvano Romano

Zsolt Gulácsi, M. Gulácsi

A detailed description of phase transitions in two dimensions is presented based on the two-dimensional classical XY model. After describing the basic physics of topological ordering, the starting model Hamiltonian is constructed for a detailed study. Following this, a direct space renormalization programme is presented. The obtained phase transition is analysed in detail based on the scaling equations. The systematic renormalization group calculation up to third order based on field-theoretical techniques is also presented. The notion of topological excitations from the viewpoint of the dual model is analysed in detail. The D > 2 cases are analysed through the three-dimensional XY model and layered systems. This article is pedagogical in nature and is intended to be accessible to any graduate student or physicist who is not an expert in this field.