Journal ArticleDOI
Lattice Statistics in a Magnetic Field. I. A Two-Dimensional Super-Exchange Antiferromagnet
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In this paper, the authors derived the partition function of a two-dimensional super-exchange antiferromagnet in an arbitrary magnetic field, which is a decorated square lattice in which magnetic Ising spins on the bonds are coupled together via non-magnetic Ising spin on the vertices.Abstract:
The partition function of a two-dimensional ` super-exchange ’ antiferromagnet in an arbitrary magnetic field is derived rigorously. The model is a decorated square lattice in which magnetic Ising spins on the bonds are coupled together via non-magnetic Ising spins on the vertices. By use of the decoration transformation all the thermodynamic and magnetic properties of the model are derived from Onsager’s solution for the standard square lattice in zero field. The transition temperature T t (H) is a single-valued, decreasing function of the field H . The energy and the magnetization are continuous functions of T for all magnetic fields; but the specific heat and the temperature gradient of the magnetization become infinite as — In | T — T t |. The initial ( H = 0) susceptibility is a continuous and smoothly varying function of T with a maximum 40 % above the critical point; but ∂x/∂ T becomes infinite at T = T c . In a non-vanishing field the susceptibility has a logarithmic infinity at T = T t . For small fields the behaviour near the critical point is given by X ≈ ( N μ/ kT ) {2—√2— D ( T—T c ) ln ∣ T — T c ∣ — D´H 2 ln ∣ T — T c ∣}, where D and D9 are constants.read more
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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.
Journal ArticleDOI
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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Relation between the specific heat and susceptibility of an antiferromagnet
TL;DR: In this paper, it was shown by a general theoretical argument that the variation of the magnetic specific heat of a simple antiferromagnet, in particular the singular behavior in the region of the transition, should be closely similar to the behaviour of the function ∂(χT)∂T, where χ is the zero-field susceptibility.
Journal ArticleDOI
Phase diagrams and critical behavior in Ising square lattices with nearest- and next-nearest-neighbor interactions
Kurt Binder,David P. Landau +1 more
TL;DR: In this article, the phase diagrams of Ising antiferromagnets in a magnetic field were investigated for various values of the ratio $R$ between nearest-and next-nearest-neighbor interaction.
References
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Antiferromagnetism. Theory of Superexchange Interaction
TL;DR: In this article, the general formalism of Kramers indicating the existence of superexchange interaction has been reduced, under simplifying assumptions, to the point where actual formulas for the interaction can be written down directly in terms of spin operators, with certain exchange and transition integrals as parameters.
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