Conjectured singularity loci for the Potts model on the square lattice
作者： J D Ramshaw
DOI: 10.1088/0305-4470/12/10/006
关键词: Chiral Potts curve 、 Gravitational singularity 、 Mathematics 、 Square lattice 、 Ising model 、 Combinatorics 、 Singularity 、 Lattice model (physics) 、 Potts model 、 Conjecture
摘要: It is conjectured that the singularities in free energy for q-state Potts model on square lattice lie two self-dual circles complex x plane where x=exp(-J/kT) usual low-temperature variable. These are natural generalisations of known Ising (q=2). The conjecture leads to prediction there a single antiferromagnetic critical point at x=1+(q/(q-1))12/.
harvard.edu
sci-hub.se 参考文章(10)
J P Straley, M E Fisher, Three-state Potts model and anomalous tricritical points Journal of Physics A: Mathematical, Nuclear and General. ,vol. 6, pp. 1310- 1326 ,(1973) , 10.1088/0305-4470/6/9/007
R Zwanzig, J D Ramshaw, Potts model specific heat critical exponents Journal of Physics A. ,vol. 10, pp. 65- 69 ,(1977) , 10.1088/0305-4470/10/1/016
H. J. Brascamp, H. Kunz, Zeroes of the partition function for the Ising model in the complex temperature plane Journal of Mathematical Physics. ,vol. 15, pp. 65- 66 ,(1974) , 10.1063/1.1666505
L. Mittag, M. J. Stephen, Dual Transformations in Many‐Component Ising Models Journal of Mathematical Physics. ,vol. 12, pp. 441- 450 ,(1971) , 10.1063/1.1665606
R J Baxter, Potts model at the critical temperature Journal of Physics C: Solid State Physics. ,vol. 6, ,(1973) , 10.1088/0022-3719/6/23/005
W. E. Brittin, B. W. Downs, Joanne Downs, Raymond J. Seeger, Lectures in Theoretical Physics American Journal of Physics. ,vol. 30, pp. 389- 389 ,(1962) , 10.1119/1.1942034
A. Hintermann, H. Kunz, F. Y. Wu, Exact results for the Potts model in two dimensions Journal of Statistical Physics. ,vol. 19, pp. 623- 632 ,(1978) , 10.1007/BF01011773
M Schick, R B Griffiths, Antiferromagnetic ordering in the three-state Potts model Journal of Physics A. ,vol. 10, pp. 2123- 2131 ,(1977) , 10.1088/0305-4470/10/12/020
Taro Kihara, Yukio Midzuno, Toshio Shizume, Statistics of Two-Dimensional Lattices with Many Components Journal of the Physical Society of Japan. ,vol. 9, pp. 681- 687 ,(1954) , 10.1143/JPSJ.9.681
R. B. Potts, Some generalized order - disorder transformations Mathematical Proceedings of the Cambridge Philosophical Society. ,vol. 48, pp. 106- 109 ,(1952) , 10.1017/S0305004100027419