Emergence of Concentration Effects in the Variational Analysis of the N-Clock Model

Cicalese, MarcoOrlando, GianlucaRuf, Matthias2022-01-012022-01-012022-01-01202210.1002/cpa.22033https://infoscience.epfl.ch/handle/20.500.14299/184187WOS:000733170500001We investigate the relationship between the N-clock model (also known as planar Potts model or DOUBLE-STRUCK CAPITAL ZN-model) and the XY model (at zero temperature) through a Gamma-convergence analysis of a suitable rescaling of the energy as both the number of particles and N diverge. We prove the existence of rates of divergence of N for which the continuum limits of the two models differ. With the aid of Cartesian currents we show that the asymptotics of the N-clock model in this regime features an energy that may concentrate on geometric objects of various dimensions. This energy prevails over the usual vortex-vortex interaction energy. (c) 2021 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.Mathematics, AppliedMathematicsMathematicsginzburg-landauspin systemslower boundsconvergencefunctionalsenergyphasemapsmetastabilitytransitionsEmergence of Concentration Effects in the Variational Analysis of the N-Clock Modeltext::journal::journal article::research article