Singularity of Nonlinear Response near the Critical Field. I : Static Case

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概要

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• Phenomenological arguments are presented to clarify the singularity of static nonlinear response near the critical magnetic (or electric) field H_c. The singularity of nonlinear susceptibility x(H) is connected with the expansion of the free energy Φ(m) as a function of a quantity (m_c-m), where m is the normalized magnetization and m_c its value at the critical field; i. e. if Φ(m)=a_0-a_1(m_c-m)+a_2(m_c-m)^<ψ…>, then x(H)~1/(H_c-H)^<γ_H>; γ_H=(ψ-2)/(ψ-1). That is, for 1<ψ<2, x(H) is continuous, for ψ=2, it is finite but discontinuous at H=H_2, and forψ>2, it is divergent. The index γ_H(or γ_E) is investigated in the one-dimensional exactly soluble magnetic systems at T=0 and the two-dimensional ferroelectric (KDP) models at finite temperature. The value of γ_H is zero for a fermion system with repulsive delta-function interaction. γ_H is equal to 1/2 for the antiferromagnetic Heisenberg model. In the Hubbard model, γ_H is equal to 1/2 in the case of half-filled band, and γ_H is always zero other-wise. In the general two-dimensional ferroelectric models, there exists no critical electric field, though the Wu model has a critical field E_c with γ_E=1/2.

• 理論物理学刊行会の論文
• 1969-11-25

著者

• Suzuki Masuo

  The Institute For Solid State Physics University Of Tokyo

• Suzuki Masuo

  The Institute For Solid State Physics The University Of Tokyo

関連論文

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• Statistical Mechanics of the Finite Ising Model with Higher Spin
• Relationship among Exactly Soluble Models of Critical Phenomena. I : 2D Ising Model, Dimer Problem and the Generalized XY-Model
• Singularity of Nonlinear Response near the Critical Field. I : Static Case
• Long-Range Order in Ideal Ferromagnets
• Theorems on Extended Ising Model with Applications to Dilute Ferromagnetism

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