Journal ArticleDOI
Two-Dimensional Ising Model as a Soluble Problem of Many Fermions
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In the absence of an external magnetic field, the Onsager method has been shown to be exactly soluble and shows a phase transition as discussed by the authors, which has attracted a lot of interest in the last few decades.Abstract:
The two-dimensional Ising model for a system of interacting spins (or for the ordering of an AB alloy) on a square lattice is one of the very few nontrivial many-body problems that is exactly soluble and shows a phase transition. Although the exact solution in the absence of an external magnetic field was first given almost twenty years ago in a famous paper by Onsager1 using the theory of Lie algebras, the flow of papers on both approximate and exact methods has remained strong to this day.2 One reason for this has been the interest in testing approximate methods on an exactly soluble problem. A second reason, no doubt, has been the considerable formidability of the Onsager method. The simplification achieved by Bruria Kaufman3 using the theory of spinor representations has diminished, but not removed, the reputation of the Onsager approach for incomprehensibility, while the subsequent application of this method by Yang4 to the calculation of the spontaneous magnetization has, if anything, helped to restore this reputation.read more
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The Renormalization group and the epsilon expansion
TL;DR: In this paper, the modern formulation of the renormalization group is explained for both critical phenomena in classical statistical mechanics and quantum field theory, and the expansion in ϵ = 4−d is explained [ d is the dimension of space (statistical mechanics) or space-time (quantum field theory)].
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The theory of equilibrium critical phenomena
TL;DR: The theory of critical phenomena in systems at equilibrium is reviewed at an introductory level with special emphasis on the values of the critical point exponents α, β, γ,..., and their interrelations as mentioned in this paper.
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The renormalization group and critical phenomena
TL;DR: In this article, a simplified presentation of the basic ideas of the renormalization group and the ε expansion applied to critical phenomena is given, following roughly a summary exposition given in 1972.
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Static Phenomena Near Critical Points: Theory and Experiment
Leo P. Kadanoff,Wolfgang Götze,David Hamblen,Robert Hecht,E. A. S. Lewis,V. V. Palciauskas,Martin Rayl,Jack Swift,D. E. Aspnes,Joseph W. Kane +9 more
TL;DR: In this paper, the authors compared theory and experiment for behavior very near critical points, and suggested that scaling laws provide a promising approach to understand phenomena near the critical point, but that they are by no means proved or disproved by the existing experimental data.
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Universal Term in the Free Energy at a Critical Point and the Conformal Anomaly
TL;DR: In this paper, it was shown that the leading finite-size correction to lnZ for a two-dimensional system at a conformally invariant critical point on a strip of length L, width β (β L ), is (π/6) c (L /β), where c is the conformal anomaly.
References
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Theory of Superconductivity
TL;DR: In this article, a theory of superconductivity is presented, based on the fact that the interaction between electrons resulting from virtual exchange of phonons is attractive when the energy difference between the electrons states involved is less than the phonon energy, and it is favorable to form a superconducting phase when this attractive interaction dominates the repulsive screened Coulomb interaction.
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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.
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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.
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Über das Paulische Äquivalenzverbot
Pascual Jordan,Eugene P. Wigner +1 more
TL;DR: In this paper, a quantenmechanik der Gasentartung is discussed, e.g., ein ideales oder nichtideales Gase, der Paulischen Aquivalenzverbot unterworfenes Gas zu beschreiben with begriffen, die keinen Bezug nehmen auf den abstrakten Koordinatenraum der Atomgesamtheit des Gases, sondern nur den gewohnlichen dreidimensionalen Raum benut
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About the Pauli exclusion principle
Pascual Jordan,Eugene P. Wigner +1 more
TL;DR: In this article, eine Fortsetzung der kurzlich von einem der Verfasser vorgelegten Note „Zur Quantenmechanik der Gasentartung“, deren Ergebnisse hier wesentlich erweitert werden.