A Theory of the Second Order Phase Transitions in Spin Systems. II : Complex Magnetic Field

概要

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The thermodynamic quantities of the Ising model are analyzed near T_c, 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)=t^λf(θ/t^<λ+γ>), assuming that the susceptibility behaves like X_<0^+>~t^<-γ> near T_c where t=T/T_c-1. It is shown that there are two types of the situation: type I, in which a critical angle θ_c(t) exists such that g(θ, t)=0 for 0≦|θ|≦θ_c, 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)=(1/2_π)ReM(iθ, t), where h=2mH/kT. g(θ, t) for an exactly soluble model near T_θ is given by the equation θ^2~t^3+a_1t^2g^2+a_2tg^4+a_3g^6(a_i<0). This is a good example for the general theory.
理論物理学刊行会の論文
1967-12-25