Heisenberg Model for the 3×3 Square Lattice

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概要

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• The exact excitation spectrum of a 3×3 two dimensional square lattice interacting via the nearest neighbour anisotropic Heisenberg Hamiltonian H=JΣ__<<ij>>{S_<i^z>S_<j^z>+γ(S_<i^x>S_<j^x>+S_<i^y>S_<j^y>)}, has been obtained for various values of the anisotropy constant γ. The zeros of the partition function in the complex μ=exp(-mH_e/k_BT) plane are calculated for different γ for both ferromagnetic (J<0) and antiferromagnetic (J>0) coupling. For 0⩽γ⩽1, the ferromagnetic zeros obey the generalized Lee-Yang theorem at all temperatures, but, for γ>1, they violate it at sufficiently low temperatures. For antiferromagnetic coupling, the zeros lie on the (unphysical) negative real axis for all values of γ and temperature. The zero-field susceptibility, for antiferromagnetic coupling, does not display a local maximum as a function of temperature in contrast to Kawabata's results on the same lattice.

• 社団法人日本物理学会の論文
• 1973-05-05

著者

• Majumdar C.

  Tata Institute Of Fundamental Research

• Krishan K.

  Tata Institute Of Fundamental Research

• Mubayi V.

  Tata Institute of Fundamental Research

関連論文

• Heisenberg Model for the 3×3 Square Lattice
• Role of Electron-Electron Interaction in the Theory of Positron Annihilation in Metals
• Positronium Formation in Interacting Electron Gas

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