2013/07/31 by Wolfgang Bietenholz, Urs Gerber, Fernando G. Rejón-Barrera
Mathematics · Physics and Astronomy · #Action (physics) #Condensed matter physics #Constraint (computer-aided design) #Geometry #Kosterlitz–Thouless transition #Lattice (music) #Materials science #Mathematical Dynamics and Fractals #Mathematics #Physics #Quantum chaos and dynamical systems #Quantum mechanics #Superconductivity #Theoretical and Computational Physics #cond-mat.stat-mech #hep-lat
paper · pdf · doi:10.1088/1742-5468/2013/12/p12009
39 pages, LaTex, 17 figures, 5 tables, final version to appear in JSTAT (Journal of Statistical Mechanics: Theory and Experiment). A section about the Binder cumulant U_4 and the second moment correlation lenght xi_2 has been added
arxiv created 2013/11/19 · openalex publication_date 2013/12/20 · arxiv updated 2015/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The 2D XY model exhibits an essential phase transition, which was predicted long ago—by Berezinskii, Kosterlitz and Thouless (BKT)—to be driven by the (un)binding of vortex–anti-vortex pairs. This transition has been confirmed for the standard lattice action, and for actions with distinct couplings, in agreement with universality. Here we study a highly unconventional formulation of this model, which belongs to the class of topological lattice actions: it does not have any couplings at all, but just a constraint for the relative angles between nearest neighbour spins. By means of dynamical boundary conditions we measure the helicity modulus ϒ, which shows that this formulation performs a BKT phase transition as well. Its finite size effects are amazingly mild, in contrast to other lattice actions. This provides one of the most precise numerical confirmations ever of a BKT transition in this model. On the other hand, up to the lattice sizes that we explored, there are deviations from the spin wave approximation, for instance for the Binder cumulant U 4 and for the leading finite size correction to ϒ. Finally we observe that the (un)binding mechanism follows the usual pattern, although free vortices do not require any energy in this formulation. Due to this observation, one should reconsider an aspect of the established picture, which estimates the critical temperature based on this energy requirement.