Phase diagram of the triangularlattice Potts antiferromagnet
Here, we study the phase diagram of the triangularlattice Qstate Potts model in the real $(Q, v)$ plane, where $$v={\rm e}^J1$$ is the temperature variable. Our first goal is to provide an obviously missing feature of this diagram: the position of the antiferromagnetic critical curve. This curve turns out to possess a bifurcation point with two branches emerging from it, entailing important consequences for the global phase diagram. We have obtained accurate numerical estimates for the position of this curve by combining the transfermatrix approach for strip graphs with toroidal boundary conditions and the recent method of critical polynomials. The second goal of this work is to study the corresponding $$A_{p1}$$ RSOS model on the torus, for integer $$p=4, 5, \ldots, 8$$ . We clarify its relation to the corresponding Potts model, in particular concerning the role of boundary conditions. For certain values of p, we identify several new critical points and regimes for the RSOS model and we initiate the study of the flows between the corresponding field theories.
 Authors:

^{[1]}
;
^{[2]}
;
^{[3]}
 PSL Research Univ., Paris (France); Sorbonne Univ., Paris (France); CEA Saclay, Gif Sur Yvette (France)
 Univ. Carlos III de Madrid, Leganes (Spain); Univ Carlos III de Madrid, Madrid (Spain)
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Publication Date:
 Report Number(s):
 LLNLJRNL751147
Journal ID: ISSN 17518113; 936039
 Grant/Contract Number:
 AC5207NA27344
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Physics. A, Mathematical and Theoretical
 Additional Journal Information:
 Journal Volume: 50; Journal Issue: 34; Journal ID: ISSN 17518113
 Publisher:
 IOP Publishing
 Research Org:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org:
 USDOE National Nuclear Security Administration (NNSA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Potts model; RSOS model; conformal field theory; transfer matrix; critical polynomial
 OSTI Identifier:
 1454617
Jacobsen, Jesper Lykke, Salas, Jesus, and Scullard, Christian R. Phase diagram of the triangularlattice Potts antiferromagnet. United States: N. p.,
Web. doi:10.1088/17518121/aa778f.
Jacobsen, Jesper Lykke, Salas, Jesus, & Scullard, Christian R. Phase diagram of the triangularlattice Potts antiferromagnet. United States. doi:10.1088/17518121/aa778f.
Jacobsen, Jesper Lykke, Salas, Jesus, and Scullard, Christian R. 2017.
"Phase diagram of the triangularlattice Potts antiferromagnet". United States.
doi:10.1088/17518121/aa778f. https://www.osti.gov/servlets/purl/1454617.
@article{osti_1454617,
title = {Phase diagram of the triangularlattice Potts antiferromagnet},
author = {Jacobsen, Jesper Lykke and Salas, Jesus and Scullard, Christian R.},
abstractNote = {Here, we study the phase diagram of the triangularlattice Qstate Potts model in the real $(Q, v)$ plane, where $v={\rm e}^J1$ is the temperature variable. Our first goal is to provide an obviously missing feature of this diagram: the position of the antiferromagnetic critical curve. This curve turns out to possess a bifurcation point with two branches emerging from it, entailing important consequences for the global phase diagram. We have obtained accurate numerical estimates for the position of this curve by combining the transfermatrix approach for strip graphs with toroidal boundary conditions and the recent method of critical polynomials. The second goal of this work is to study the corresponding $A_{p1}$ RSOS model on the torus, for integer $p=4, 5, \ldots, 8$ . We clarify its relation to the corresponding Potts model, in particular concerning the role of boundary conditions. For certain values of p, we identify several new critical points and regimes for the RSOS model and we initiate the study of the flows between the corresponding field theories.},
doi = {10.1088/17518121/aa778f},
journal = {Journal of Physics. A, Mathematical and Theoretical},
number = 34,
volume = 50,
place = {United States},
year = {2017},
month = {7}
}