On the Onsager-Yang-value of the spontaneous magnetization
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In this article, it was shown that the value of spontaneous magnetization for the two-dimensional Ising model computed by Onsager is indeed, the appropriate derivative of the free energy with respect to the magnetic field.Abstract:
We show that the value of the spontaneous magnetization for the two-dimensional Ising model computed by Onsager is indeed, the appropriate derivative of the free energy with respect to the magnetic field. The argument is based on a simple application of the duality transformation.read more
Citations
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Toeplitz matrices and toeplitz determinants under the impetus of the ising model: Some history and some recent results
TL;DR: In this paper, the authors discuss the crucial role of the two-dimensional Ising model in stimulating the development of the theory of Toeplitz determinants and their applications.
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Interface profile of the Ising ferromagnet in two dimensions
Douglas B. Abraham,P. Reed +1 more
TL;DR: In this paper, the interface profile of the two-dimensional Ising ferromagnet is obtained for all temperatures in the thermodynamic limit, and the width of the interface depends on its length as (length) 1/2.
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Zeroes of the partition function for the Ising model in the complex temperature plane
H. J. Brascamp,H. Kunz +1 more
TL;DR: For special boundary conditions, the zeroes of the partition function of the square Ising model are shown to lie on Fisher's two circles in the complex exp(− 2βJ) plane as discussed by the authors.
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Critical region for droplet formation in the two-dimensional ising model
TL;DR: In this article, the formation/dissolution of equilibrium droplets in finite systems at parameters corresponding to phase coexistence was studied, and it was shown that the critical scaling for droplet formation and dissolution is when vL3/2L−2 tends to a definite limit.
Book
Statistical Mechanics and the Physics of Many-Particle Model Systems
TL;DR: In this article, the concepts of broken symmetry, quantum protectorate, and quasi-averages are analyzed in the context of quantum theory of magnetism and theory of superconductivity.
References
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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.
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Duality in Generalized Ising Models and Phase Transitions without Local Order Parameters
TL;DR: In this paper, the authors define a class of Ising models on d-dimensional lattices characterized by a number n = 1, 2, …, d (n = 1 corresponds to the Ising model with two-spin interaction).
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On the theory of cooperative phenomena in crystals
TL;DR: In this paper, the theory of cooperative phenomena in crystals is studied and the authors propose a method to solve the problem of cooperative phenomenon in crystals, which is based on the concept of cooperation.
Journal ArticleDOI
Determination of an Operator Algebra for the Two-Dimensional Ising Model
Leo P. Kadanoff,Horacio Ceva +1 more
TL;DR: In this article, the critical indices for the two-dimensional Ising model were derived from an assumed form of an operator algebra which describes how the product of two fluctuating variables may be reduced to a linear combination of the basic variables.