scholarly journals Large-q expansion of the two-dimensional q-state Potts model by the finite lattice method

1999 ◽  
Vol 73 (1-3) ◽  
pp. 754-756
Author(s):  
H. Arisue ◽  
K. Tabata
Keyword(s):  
Potts Model ◽  
Finite Lattice ◽  
Two Dimensional ◽  
Lattice Method

Improved finite-lattice method for estimating the zero-temperature properties of two-dimensional lattice models

1996 ◽  
Vol 74 (1-2) ◽  
pp. 54-64 ◽  
Author(s):  
D. D. Betts ◽  
S. Masui ◽  
N. Vats ◽  
G. E. Stewart
Keyword(s):  
Spontaneous Magnetization ◽  
Finite Lattice ◽  
Quantum Spin ◽  
Square Lattice ◽  
Two Dimensional ◽  
Zero Temperature ◽  
Quantum Spin Systems ◽  
Lattice Method ◽  
Dimensional Lattice ◽  
Finite Lattices

The well-known finite-lattice method for the calculation of the properties of quantum spin systems on a two-dimensional lattice at zero temperature was introduced in 1978. The method has now been greatly improved for the square lattice by including finite lattices based on parallelogram tiles as well as the familiar finite lattices based on square tiles. Dozens of these new finite lattices have been tested and graded using the [Formula: see text] ferromagnet. In the process new and improved estimates have been obtained for the XY model's ground-state energy per spin, ε0 = −0.549 36(30) and spontaneous magnetization per spin, m = 0.4349(10). Other properties such as near-neighbour, zero-temperature spin–spin correlations, which appear not to have been calculated previously, have been estimated to high precision. Applications of the improved finite-lattice method to other models can readily be carried out.

scholarly journals Geometrical four-point functions in the two-dimensional critical Q-state Potts model: the interchiral conformal bootstrap

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yifei He ◽  
Jesper Lykke Jacobsen ◽  
Hubert Saleur
Keyword(s):  
Potts Model ◽  
Correlation Functions ◽  
Liouville Theory ◽  
Analytical Determination ◽  
Conformal Weight ◽  
Two Dimensional ◽  
Conformal Blocks ◽  
Conformal Bootstrap ◽  
Point Correlation

Abstract Based on the spectrum identified in our earlier work [1], we numerically solve the bootstrap to determine four-point correlation functions of the geometrical connectivities in the Q-state Potts model. Crucial in our approach is the existence of “interchiral conformal blocks”, which arise from the degeneracy of fields with conformal weight hr,1, with r ∈ ℕ*, and are related to the underlying presence of the “interchiral algebra” introduced in [2]. We also find evidence for the existence of “renormalized” recursions, replacing those that follow from the degeneracy of the field $$ {\Phi}_{12}^D $$ Φ 12 D in Liouville theory, and obtain the first few such recursions in closed form. This hints at the possibility of the full analytical determination of correlation functions in this model.

Phase transition of a two-dimensional, multiplicatively coupledXY–Potts model

2009 ◽  
Vol 42 (22) ◽  
pp. 225001 ◽  
Author(s):  
Marcel Hellmann ◽  
Youjin Deng ◽  
Matthias Weiss ◽  
Dieter W Heermann
Keyword(s):  
Phase Transition ◽  
Potts Model ◽  
Two Dimensional

Evidence for universality of the potts model on the two-dimensional penrose lattice

1988 ◽  
Vol 126 (8-9) ◽  
pp. 471-475 ◽  
Author(s):  
William G. Wilson ◽  
Chester A. Vause
Keyword(s):  
Potts Model ◽  
Two Dimensional
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