The Nclock model is a twodimensional ferromagnetic spin model on the square lattice in which the spin field is constrained to take values in a set of N equispaced points of the unit circle. It is usually considered as an approximation of the XY model, for which instead the spin field is allowed to attain all the values of the unit circle. In the theory of superconductivity the latter models phase transitions mediated by the formation and the interaction of codimension 2 topological defects as in the wellknown GinzburgLandau functional. A breakthrough result by Fröhlich and Spencer (CMP 1981) shows that the same kind of phase transitions appear in the Nclock model for N large enough. By a variational analysis we find the explicit rate of divergence of N (with respect to the number of interacting lattice points) for which low energy configurations of the Nclock model asymptotically behave like those of the XY model at zero temperature. We moreover exhaustively discuss all the other regimes of N and we show how Cartesian Currents can detect the energy concentration on sets of codimenion smaller or equal than 2. The results presented are contained in a series of recent papers in collaboration with G. Orlando (Poliba) and M. Ruf (EPFL).
You are here
Does the Nclock model approximate the XY model?
Marco Cicalese
Schedule:
Tuesday, March 2, 2021  15:00 to 16:00
Location:
Online
Abstract:
Openings
 Public Calls for Professors
 Temporary Professors/Researchers/Visiting Professors
 SISSA Mathematical Fellowships
 PostLauream Fellowships
 Research Training Fellowships
 Marie SklodowskaCurie Grants
 Open positions in MathLab
 Post Doctoral Fellowships
 PhD Scolarships
 SIS Fellowships
 Undergraduate Fellowships
 Postgraduate Fellowships
 MSc in Mathematics
 MSc in Data Science and Scientific Computing (DSSC)
 Professional Master Courses
 SISSA Mathematics Medals
Upcoming events

Hamza Ounesli
"Cossa xe... a measure of maximal entropy?"
Friday, April 23, 2021  11:00 to 12:00

Alexander Alexandrov
KP integrability of triple Hodge integrals
Wednesday, May 5, 2021  11:00 to 12:00

Gennady El
Riemann problem for the BenjaminBonaMahony equation
Wednesday, May 19, 2021  16:00 to 17:00
Today's Lectures

09:30 to 11:00

14:00 to 16:00

14:00 to 16:00
Recent publications

G.P. Leonardi; G. Saracco,Rigidity and trace properties...

G. Saracco,A sufficient criterion to dete...

D. Agostinelli; A. DeSimone; G. Noselli,Nutations in plant shoots: End...

D. Agostinelli; G. Noselli; A. DeSimone,Nutations in growing plant sho...