Classical topological paramagnetism

R. Bondesan, Z. Ringel

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Topological phases of matter are one of the hallmarks of quantum condensed matter physics. One of their striking features is a bulk-boundary correspondence wherein the topological nature of the bulk manifests itself on boundaries via exotic massless phases. In classical wave phenomena, analogous effects may arise; however, these cannot be viewed as equilibrium phases of matter. Here, we identify a set of rules under which robust equilibrium classical topological phenomena exist. We write simple and analytically tractable classical lattice models of spins and rotors in two and three dimensions which, at suitable parameter ranges, are paramagnetic in the bulk but nonetheless exhibit some unusual long-range or critical order on their boundaries. We point out the role of simplicial cohomology as a means of classifying, writing, and analyzing such models. This opens an experimental route for studying strongly interacting topological phases of spins.

Original languageAmerican English
Article number174418
JournalPhysical Review B
Issue number17
StatePublished - 11 May 2017
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2017 uk. Published by the American Physical Society.


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