TY - JOUR

T1 - Γ-Convergence Analysis of a Generalized XY Model

T2 - Fractional Vortices and String Defects

AU - Badal, Rufat

AU - Cicalese, Marco

AU - De Luca, Lucia

AU - Ponsiglione, Marcello

N1 - Publisher Copyright:
© 2017, Springer-Verlag GmbH Germany.

PY - 2018/3/1

Y1 - 2018/3/1

N2 - We propose and analyze a generalized two dimensional XY model, whose interaction potential has n weighted wells, describing corresponding symmetries of the system. As the lattice spacing vanishes, we derive by Γ -convergence the discrete-to-continuum limit of this model. In the energy regime we deal with, the asymptotic ground states exhibit fractional vortices, connected by string defects. The Γ -limit takes into account both contributions, through a renormalized energy, depending on the configuration of fractional vortices, and a surface energy, proportional to the length of the strings. Our model describes in a simple way several topological singularities arising in Physics and Materials Science. Among them, disclinations and string defects in liquid crystals, fractional vortices and domain walls in micromagnetics, partial dislocations and stacking faults in crystal plasticity.

AB - We propose and analyze a generalized two dimensional XY model, whose interaction potential has n weighted wells, describing corresponding symmetries of the system. As the lattice spacing vanishes, we derive by Γ -convergence the discrete-to-continuum limit of this model. In the energy regime we deal with, the asymptotic ground states exhibit fractional vortices, connected by string defects. The Γ -limit takes into account both contributions, through a renormalized energy, depending on the configuration of fractional vortices, and a surface energy, proportional to the length of the strings. Our model describes in a simple way several topological singularities arising in Physics and Materials Science. Among them, disclinations and string defects in liquid crystals, fractional vortices and domain walls in micromagnetics, partial dislocations and stacking faults in crystal plasticity.

UR - http://www.scopus.com/inward/record.url?scp=85033443424&partnerID=8YFLogxK

U2 - 10.1007/s00220-017-3026-3

DO - 10.1007/s00220-017-3026-3

M3 - Article

AN - SCOPUS:85033443424

SN - 0010-3616

VL - 358

SP - 705

EP - 739

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 2

ER -