Color-dependent interactions in the three coloring model


Type
Article
Change log
Authors
Verpoort, PC 
Simmons, J 
Castelnovo, Claudio  ORCID logo  https://orcid.org/0000-0003-1752-6343
Abstract

Since it was first discussed by Baxter in 1970, the three coloring model has been studied in several contexts, from frustrated magnetism to superconducting devices and glassiness. In presence of interactions, when the model is no longer exactly soluble, it was already observed that the phase diagram is highly nontrivial. Here we discuss the generic case of "color-dependent" nearest-neighbor interactions between the vertex chiralities. We uncover different critical regimes merging into one another: c=1/2 free fermions combining into c=1 free bosons; c=1 free bosons combining into c=2 critical loop models; as well as three separate c=1/2 critical lines merging at a supersymmetric c=3/2 critical point. When the three coupling constants are tuned to equal one another, transfer-matrix calculations highlight a puzzling regime where the central charge appears to vary continuously from 3/2 to 2.

Description
Keywords
cond-mat.stat-mech, cond-mat.stat-mech, 82B20
Journal Title
Physical Review B
Conference Name
Journal ISSN
2469-9950
2469-9969
Volume Title
98
Publisher
American Physical Society
Sponsorship
Engineering and Physical Sciences Research Council (EP/M007065/1)
This work was supported in part by Engineering and Physical Sciences Research Council (EPSRC) Grant No. GR/R83712/01 and by EPSRC Postdoctoral Research Fellowship EP/G049394/1 (C. Castelnovo), and by EPSRC Grant No. EP/D070643/1 (JJHS). P. Verpoort acknowledges funding by the Studienstiftung des deutschen Volkes.