Author
L. Mittag
Bio: L. Mittag is an academic researcher. The author has contributed to research in topics: Lattice (order) & Square lattice. The author has an hindex of 1, co-authored 1 publications receiving 101 citations.
Papers
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TL;DR: In this article, dual transformations in many-component Ising models in two dimensions on a square lattice are studied from both a topological and an algebraic point of view.
Abstract: Dual transformations in many‐component Ising models in two dimensions on a square lattice are studied. The models considered include those of Ashkin and Teller and of Potts. In certain cases the dual transformation is a relation between the partition function of a lattice at high and low temperatures and can be used to determine a unique critical temperature if one exists. Dual transformations are considered both from a topological and an algebraic point of view. The topological arguments are a natural extension of those used by Onsager for the 2‐component Ising model. The transfer matrices for these models are constructed, and it is shown how the dual transformation arises in this formulation of the problem. The algebras generated by these models are investigated and provide a generalization of the spinor algebra introduced by Kaufman in the 2‐component Ising model.
107 citations
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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.
Abstract: This is a tutorial review on the Potts model aimed at bringing out in an organized fashion the essential and important properties of the standard Potts model. Emphasis is placed on exact and rigorous results, but other aspects of the problem are also described to achieve a unified perspective. Topics reviewed include the mean-field theory, duality relations, series expansions, critical properties, experimental realizations, and the relationship of the Potts model with other lattice-statistical problems.
2,964 citations
TL;DR: In this article, it was shown that the two-dimensional q-component Potts model is equivalent to a staggered ice-type model, and it was deduced that the model has a first-order phase transition for q>4, and a higher-order transition for Q
Abstract: It is shown that the two-dimensional q-component Potts model is equivalent to a staggered ice-type model. It is deduced that the model has a first-order phase transition for q>4, and a higher-order transition for q
559 citations
TL;DR: In this paper, Bethe ansatz equations are formulated and solved numerically for eigenstates of the XXZ Hamiltonian on a finite chain with periodic boundary conditions and with a generalized class of twisted boundary conditions.
256 citations
TL;DR: In this article, a universality argument is used to describe the relationship among correlation functions in different models each of which has a line of continuously varying critical behavior, and the correlation functions for the Baxter and Ashkin-Teller models are evaluated in terms of the known spin wave and vortex correlations of a d = 2 Gaussian model.
245 citations
TL;DR: In this paper, the critical behavior of the q-state Potts model was investigated using finite-size scaling and transfer matrix methods, and an effective algorithm to compute the dominant eigenvalues of this essentially nonsymmetric transfer matrix was developed.
Abstract: We investigate the critical behaviour of the two-dimensional, q-state Potts model, using finite-size scaling and transfer matrix methods. For the continuous transition range (0 These results for continuous q were obtained from a transfer matrix constructed for a generalized Whitney polynomial representing the Potts models. An effective algorithm to compute the dominant eigenvalues of this essentially nonsymmetric transfer matrix is developed.
218 citations