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Correlation functions in the two-dimensional Ising model in a magnetic field at T = Tc

Gesualdo Delfino A, P. Simonetti

arXiv:hep-th/9605065Physics Letters BSep 1, 199667 citations

Thermodynamics of an anisotropic boundary of a two-dimensional Ising model

Helen Au-Yang

We consider a semi-infinite two-dimensional Ising model with its spins on the boundary row having a different interaction energy E′1 from the ferromagnetic bulk. We find that the boundary specific heat has two divergent terms: one of which diverges linearly at the bulk critical temperature Tc, and the other, logaritmically. The linearly divergent term is independent of E′1, and the coefficient of the logaritmically divergent term is a decreasing function of E′1. There is a boundary latent heat at Tc, which is identical to McCoy and Wu's result. The boundary spins, which can be either ferromagnetic or antiferromagnetic, are aligned for temperature lower than Tc. The boundary spontaneous magnetization approaches zero in the form of A(E′1)(1−T/Tc)1/2, and the boundary zero field magnetic susceptibility diverges at Tc in the form −B (E′1)ln|1−T/Tc|, where A(E′1) and B(E′) are increasing functions of E′1.We consider a semi-infinite two-dimensional Ising model with its spins on the boundary row having a different interaction energy E′1 from the ferromagnetic bulk. We find that the boundary specific heat has two divergent terms: one of which diverges linearly at the bulk critical temperature Tc, and the other, logaritmically. The linearly divergent term is independent of E′1, and the coefficient of the logaritmically divergent term is a decreasing function of E′1. There is a boundary latent heat at Tc, which is identical to McCoy and Wu's result. The boundary spins, which can be either ferromagnetic or antiferromagnetic, are aligned for temperature lower than Tc. The boundary spontaneous magnetization approaches zero in the form of A(E′1)(1−T/Tc)1/2, and the boundary zero field magnetic susceptibility diverges at Tc in the form −B (E′1)ln|1−T/Tc|, where A(E′1) and B(E′) are increasing functions of E′1.

Journal of Mathematical PhysicsJul 1, 197362 citations

New results for the susceptibility of the two-dimensional Ising model at criticality

Xiang‐Peng Kong, Helen Au-Yang, Jacques H. H. Perk

Physics Letters AMay 1, 198623 citations

Zero-Field Susceptibility of the Two-Dimensional Ising Model near T c

Eytan Barouch, Barry M. McCoy, Tai Tsun Wu

We compute exactly the four coefficients ${C}_{0\ifmmode\pm\else\textpm\fi{}}$ and ${C}_{1\ifmmode\pm\else\textpm\fi{}}$ in the expansion ${\ensuremath{\beta}}^{\ensuremath{-}1}\ensuremath{\chi}={C}_{0\ifmmode\pm\else\textpm\fi{}}{|1\ensuremath{-}\frac{{T}_{c}}{T}|}^{\ensuremath{-}\frac{7}{4}}+{C}_{1\ifmmode\pm\else\textpm\fi{}}{|1\ensuremath{-}\frac{{T}_{c}}{T}|}^{\ensuremath{-}\frac{3}{4}}+O(1)$ for the susceptibility of the rectangular two-dimensional Ising model.We compute exactly the four coefficients ${C}_{0\ifmmode\pm\else\textpm\fi{}}$ and ${C}_{1\ifmmode\pm\else\textpm\fi{}}$ in the expansion ${\ensuremath{\beta}}^{\ensuremath{-}1}\ensuremath{\chi}={C}_{0\ifmmode\pm\else\textpm\fi{}}{|1\ensuremath{-}\frac{{T}_{c}}{T}|}^{\ensuremath{-}\frac{7}{4}}+{C}_{1\ifmmode\pm\else\textpm\fi{}}{|1\ensuremath{-}\frac{{T}_{c}}{T}|}^{\ensuremath{-}\frac{3}{4}}+O(1)$ for the susceptibility of the rectangular two-dimensional Ising model.

Physical Review LettersDec 3, 1973238 citations

Low temperature susceptibility exponent for the three dimensional Ising model

Anthony John Guttmann, Colin J. Thompson

Physics Letters AFeb 1, 196912 citations

A Theory of the Second Order Phase Transitions in Spin Systems. II

Masuo Suzuki

The thermodynamic quantities of the Ising model are analyzed near Tc, using the asymptotic distribution function g(θ, t) of zeros for the partition function on a unit circle in the plane of the complex magnetic field. The distribution function is derived as g(θ, t) = tλf(θ/tλ + γ), assuming that the susceptibility behaves like χ0+ ∼ t-γ near Tc where t = T/Tc-1. It is shown that there are two types of the situation; type I, in which a critical angle θc(t) exists such that g(θ, t) = 0 for 0 ≦ |θ| ≦ θc, and type II, in which there is no critical angle. The critical indices are related to one another, using the above g(θ, t). The relation between the magnetic equation of state M = M(h, t) and the distribution function is given as follows: g(θ, t) = (1/2π)Re M(iθ, t), where h = 2mH/kT. g(θ, t) for an exactly soluble model near Tc is given by the equation θ2 ∼ t3 + a1t2g2 + a2tg4 + a3g6 (ai > 0). This is a good example for the general theory.The thermodynamic quantities of the Ising model are analyzed near Tc, using the asymptotic distribution function g(θ, t) of zeros for the partition function on a unit circle in the plane of the complex magnetic field. The distribution function is derived as g(θ, t) = tλf(θ/tλ + γ), assuming that the susceptibility behaves like χ0+ ∼ t-γ near Tc where t = T/Tc-1. It is shown that there are two types of the situation; type I, in which a critical angle θc(t) exists such that g(θ, t) = 0 for 0 ≦ |θ| ≦ θc, and type II, in which there is no critical angle. The critical indices are related to one another, using the above g(θ, t). The relation between the magnetic equation of state M = M(h, t) and the distribution function is given as follows: g(θ, t) = (1/2π)Re M(iθ, t), where h = 2mH/kT. g(θ, t) for an exactly soluble model near Tc is given by the equation θ2 ∼ t3 + a1t2g2 + a2tg4 + a3g6 (ai > 0). This is a good example for the general theory.

Progress of Theoretical PhysicsDec 1, 196762 citations

Zero-Field Susceptibility of the Two-Dimensional Ising Model near Tc .

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Zero-Field Susceptibility of the Two-Dimensional Ising Model near Tc .

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