Condensed Matter Theory Seminar | April 04, 14:00
Forgetting boundaries: A geometric approach to confined critical systems
What would you do if you were a system at criticality? You would of course
forget about the microscopic length scales (say lattice spacing). But if you
were in a confined system you would also try to loose track of the
boundaries. The implementation of above requirement in absolute geometric
language leads us to the fractional Yamabe problem. We are looking, within
the class of metrics differing from the starting flat one by a local
rescaling factor, for a metric making a generalized (anomalous in physics
vernacular) notion of curvature constant. This approach which we dub
"Critical Geometry" leads to novel, testable and succesfully tested
prediction in d>2 systems.
[1] (foundation & Ising 3d) GG, A Trombettoni [arXiv:1904.08919]
[2] (upper critical dim) A Galvani, GG, A Trombettoni [arXiv:2103.12449]
[3] (3d XY) A Galvani, GG, A Trombettoni [arXiv:2108.03488]
[4] (3d percolation) A Galvani, A Trombettoni, GG [arXiv:2110.13232]
Heidelberg University
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Contact: Silvia Pappalardi