Physics – Mathematical Physics
Scientific paper
2009-07-31
Physics
Mathematical Physics
Scientific paper
We introduce and discuss discrete two-dimensional models for XY spin systems and screw dislocations in crystals. We prove that, as the lattice spacing $\e$ tends to zero, the relevant energies in these models behave like a free energy in the complex Ginzburg-Landau theory of superconductivity, justifying in a rigorous mathematical language the analogies between screw dislocations in crystals and vortices in superconductors. To this purpose, we introduce a notion of asymptotic variational equivalence between families of functionals in the framework of $\Gamma$-convergence. We then prove that, in several scaling regimes, the complex Ginzburg-Landau, the XY spin system and the screw dislocation energy functionals are variationally equivalent. Exploiting such an equivalence between dislocations and vortices, we can show new results concerning the asymptotic behavior of screw dislocations in the $|\log\e|^2$ energetic regime.
Alicandro Roberto
Cicalese Marco
Ponsiglione Marcello
No associations
LandOfFree
Variational equivalence between Ginzburg-Landau, XY spin systems and screw dislocations energies does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Variational equivalence between Ginzburg-Landau, XY spin systems and screw dislocations energies, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Variational equivalence between Ginzburg-Landau, XY spin systems and screw dislocations energies will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-267840