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Title: Phase diagram of the triangular-lattice Potts antiferromagnet

Abstract

Here, we study the phase diagram of the triangular-lattice Q-state Potts model in the real $(Q, v)$ -plane, where $$v={\rm e}^J-1$$ 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 transfer-matrix 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 $$A_{p-1}$$ 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:
ORCiD logo [1]; ORCiD logo [2];  [3]
  1. PSL Research Univ., Paris (France); Sorbonne Univ., Paris (France); CEA Saclay, Gif Sur Yvette (France)
  2. Univ. Carlos III de Madrid, Leganes (Spain); Univ Carlos III de Madrid, Madrid (Spain)
  3. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1454617
Report Number(s):
LLNL-JRNL-751147
Journal ID: ISSN 1751-8113; 936039; TRN: US1901093
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Physics. A, Mathematical and Theoretical
Additional Journal Information:
Journal Volume: 50; Journal Issue: 34; Journal ID: ISSN 1751-8113
Publisher:
IOP Publishing
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Potts model; RSOS model; conformal field theory; transfer matrix; critical polynomial

Citation Formats

Jacobsen, Jesper Lykke, Salas, Jesus, and Scullard, Christian R. Phase diagram of the triangular-lattice Potts antiferromagnet. United States: N. p., 2017. Web. doi:10.1088/1751-8121/aa778f.
Jacobsen, Jesper Lykke, Salas, Jesus, & Scullard, Christian R. Phase diagram of the triangular-lattice Potts antiferromagnet. United States. https://doi.org/10.1088/1751-8121/aa778f
Jacobsen, Jesper Lykke, Salas, Jesus, and Scullard, Christian R. Fri . "Phase diagram of the triangular-lattice Potts antiferromagnet". United States. https://doi.org/10.1088/1751-8121/aa778f. https://www.osti.gov/servlets/purl/1454617.
@article{osti_1454617,
title = {Phase diagram of the triangular-lattice Potts antiferromagnet},
author = {Jacobsen, Jesper Lykke and Salas, Jesus and Scullard, Christian R.},
abstractNote = {Here, we study the phase diagram of the triangular-lattice Q-state Potts model in the real $(Q, v)$ -plane, where $v={\rm e}^J-1$ 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 transfer-matrix 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 $A_{p-1}$ 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 = {10.1088/1751-8121/aa778f},
url = {https://www.osti.gov/biblio/1454617}, journal = {Journal of Physics. A, Mathematical and Theoretical},
issn = {1751-8113},
number = 34,
volume = 50,
place = {United States},
year = {2017},
month = {7}
}

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Cited by: 3 works
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    Works referencing / citing this record:

    On the correspondence between boundary and bulk lattice models and (logarithmic) conformal field theories
    journal, November 2017


    Torus partition function of the six-vertex model from algebraic geometry
    journal, March 2019