Journal ArticleDOI
Colorings of a Hexagonal Lattice
TLDR
The number of ways of coloring the bonds of a hexagonal lattice of L sites (L large) with three colors so that no adjacent bonds are colored alike is calculated exactly, giving W = 1.20872.Abstract:
The number of ways WL of coloring the bonds of a hexagonal lattice of L sites (L large) with three colors so that no adjacent bonds are colored alike is calculated exactly, giving W = 1.20872 …. This is equivalent to counting the number of 4‐colorings of the faces of the lattice and can also be regarded as a multiple‐dimer problem. If one introduces activities corresponding to certain vertex configurations, then the system is found to have an infinite‐order phase transition between two ordered states.read more
Citations
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The Potts model
TL;DR: In this paper, a tutorial review on the Potts model is presented aimed at bringing out the essential and important properties of the standard Potts models, focusing on exact and rigorous results, but other aspects of the problem are also described to achieve a unified perspective.
Journal ArticleDOI
Hard hexagons: exact solution
TL;DR: The hard-hexagon model in lattice statistics (i.e. the triangular lattice gas with nearest-neighbour exclusion) has been solved exactly as mentioned in this paper, and a restricted class of square-lattice models with non-zero diagonal interactions can be solved.
Journal ArticleDOI
Solvable eight-vertex model on an arbitrary planar lattice
TL;DR: In this paper, it was shown that the Kagome lattice model can be solved exactly in the thermodynamic limit, its local properties at a particular site being those of a related square lattice.
Book
The Bethe Wavefunction
TL;DR: Gaudin's La fonction d'onde de Bethe as discussed by the authors is a uniquely influential masterpiece on exactly solvable models of quantum mechanics and statistical physics and is available in English for the first time.
Journal ArticleDOI
Absence of phase transition for antiferromagnetic Potts models via the Dobrushin uniqueness theorem
Jesús Salas,Alan D. Sokal +1 more
TL;DR: In this paper, it was shown that the q-state Potts antiferromagnet on a lattice of maximum coordination number r exhibits exponential decay of correlations uniformly at all temperatures (including zero temperature) whenever q>2r.
References
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Journal ArticleDOI
Exact analysis of an interacting bose gas. i. the general solution and the ground state
Elliott H. Lieb,Werner Liniger +1 more
TL;DR: In this paper, the ground-state energy as a function of γ was derived for all γ, except γ = 0, and it was shown that Bogoliubov's perturbation theory is valid when γ is small.
Journal ArticleDOI
Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model in One Dimension
Elliott H. Lieb,F. Y. Wu +1 more
TL;DR: In this paper, the short-range, one-band model for electron correlations in a narrow energy band is solved exactly in the one-dimensional case, and the ground-state energy, wave function, and chemical potentials are obtained, and it is found that the ground state exhibits no conductor-insulator transition as the correlation strength is increased.
Journal ArticleDOI
Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction
TL;DR: In this paper, the ground-state problem of spin-textonehalf{} fermions is reduced to a generalized Fredholm equation, in a generalized form, by using Bethe's hypothesis.
Journal ArticleDOI
Dimer Statistics and Phase Transitions
TL;DR: In this article, it was shown that the configurational partition function of a generalized dimer system can be expressed in terms of a Pfaffian, and hence calculated explicitly, if the lattice graph is planar and if the dimers occupy all lattice sites.
Journal ArticleDOI
One-Dimensional Chain of Anisotropic Spin-Spin Interactions. I. Proof of Bethe's Hypothesis for Ground State in a Finite System
Chen Ning Yang,C. P. Yang +1 more
TL;DR: Bethe's hypothesis for the ground state of a one-dimensional cyclic chain of anisotropic nearest-neighbor spin-spin interactions was proved for any fixed number of down spins as mentioned in this paper.