TY - JOUR
T1 - Two-dimensional Potts antiferromagnets with a phase transition at arbitrarily large q
AU - Huang, Yuan
AU - Chen, Kun
AU - Deng, Youjin
AU - Jacobsen, Jesper Lykke
AU - Kotecký, Roman
AU - Salas, Jesús
AU - Sokal, Alan D.
AU - Swart, Jan M.
PY - 2013/1/24
Y1 - 2013/1/24
N2 - We exhibit infinite families of two-dimensional lattices (some of which are triangulations or quadrangulations of the plane) on which the q-state Potts antiferromagnet has a finite-temperature phase transition at arbitrarily large values of q. This unexpected result is proven rigorously by using a Peierls argument to measure the entropic advantage of sublattice long-range order. Additional numerical data are obtained using transfer matrices, Monte Carlo simulation, and a high-precision graph-theoretic method.
AB - We exhibit infinite families of two-dimensional lattices (some of which are triangulations or quadrangulations of the plane) on which the q-state Potts antiferromagnet has a finite-temperature phase transition at arbitrarily large values of q. This unexpected result is proven rigorously by using a Peierls argument to measure the entropic advantage of sublattice long-range order. Additional numerical data are obtained using transfer matrices, Monte Carlo simulation, and a high-precision graph-theoretic method.
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U2 - 10.1103/PhysRevE.87.012136
DO - 10.1103/PhysRevE.87.012136
M3 - Article
C2 - 23410312
AN - SCOPUS:84873034404
SN - 1539-3755
VL - 87
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
IS - 1
M1 - 012136
ER -