Journal ArticleDOI
Two-Dimensional Hydrogen Bonded Crystals without the Ice Rule
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In this article, the singularities of the ground state energy of a related ring of interacting spins were found for 2D hydrogen-bonded crystals obeying the ice rule.Abstract:
Models of 2‐dimensional hydrogen bonded crystals obeying the ice rule, which previously have been solved exactly, are generalized by removing the ice rule. Many of the peculiar and unique properties of the solutions for the constrained models are now explained by showing that these models, above critical temperature, are equivalent to new unconstrained models at critical temperature. In addition to locating the critical temperature for the general but unsolved models, we locate the singularities of the ground state energy of a related ring of interacting spins.read more
Citations
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Spin glasses from vertex models
TL;DR: The transfer matrix of the inhomogeneous six-vertex model is shown to generate a one-dimensional Heisenberg spin-glass Hamiltonian through the Baxter-Luscher identity.
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Strong-interaction approximation for transfer matrix method
TL;DR: In this article, the transfer matrix of quantum spin systems is derived using transfer-matrix method and a correspondence between classical spin systems and six-vertex quantum spin system is considered.
Book ChapterDOI
The Periodic Anisotropic Spin-$$\frac{1}{2}$$ Chains
TL;DR: In this paper, the exact solution of the spin-\(\frac{1}{2}\) Heisenberg chain model was obtained and the physical properties of this model were studied.
Journal ArticleDOI
Algebraic Bethe ansatz for a spin-½ quantum linear chain with competing interactions
TL;DR: In this paper, a generalization of the formula that gives an integrable quantum 1D spin Hamiltonian with nearest-neighbour interactions as a logarithmic derivative of a vertex model transfer matrix was proposed.
References
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Journal ArticleDOI
Crystal statistics. I. A two-dimensional model with an order-disorder transition
TL;DR: In this article, the eigenwert problem involved in the corresponding computation for a long strip crystal of finite width, joined straight to itself around a cylinder, is solved by direct product decomposition; in the special case $n=\ensuremath{\infty}$ an integral replaces a sum.
Journal ArticleDOI
Two soluble models of an antiferromagnetic chain
TL;DR: In this article, two genuinely quantum models for an antiferromagnetic linear chain with nearest neighbor interactions are constructed and solved exactly, in the sense that the ground state, all the elementary excitations and the free energy are found.
Journal ArticleDOI
Statistics of the Two-Dimensional Ferromagnet. Part II
H. A. Kramers,G. H. Wannier +1 more
TL;DR: In this article, the Ising model of ferromagnetism is treated by rigorous Boltzmann statistics, and a method is developed which yields the partition function as the largest eigenvalue of some finite matrix, as long as the manifold is only one dimensionally infinite.
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.
Journal ArticleDOI
Exact Solution of the Problem of the Entropy of Two-Dimensional Ice
TL;DR: In this article, the authors consider the problem of determining the position of a hydrogen atom relative to an oxygen atom in a periodic crystal lattice, where the hydrogen atoms are not at the centers of the bonds, however, so that there are two possible states for each bond corresponding to the two positions of the hydrogen atom.