著者

橋爪 邦夫

出版者

近畿大学工学部

雑誌

近畿大学工学部研究報告 (ISSN:0386491X)

巻号頁・発行日

no.45, pp.149-171, 2011

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[Synopsis] The energy Hamiltonian, given by Heisenberg in 1928, to discuss the physical properties and the atomics tructure of ferromagnetic substance is as follows: H=—2Σ__<ij>J_<ij>S_i・S_j.-gβΣ__iS_i・H. A spinv ariable S_i is associated with each lattice site. In the Ising model of J_<ijx>=J_<ijy>=0 and J_<iijz>≠0, proposed by E. Ising in Zeit. Phys. 31 253(1925), the above Hamiltonian is simplified as follows : H=-2Σ__<ij>J_<ij>S_<iz>S_<jz>-gβHΣ__iS_<iz>・S_<iz>=±1/2. The system is an array of N fixed points calld lattice sites that form an n-dimensional periodic lattice. The energy of the system in the configuration specified by {S_i} is as follows : E{S_i}=εΣ__<ij>S_iS_j-βHΣ__iS. S_i=+1 denotes that the ith site has spin ip and S_i=-1 detotes that the ith site has spin down. The partition function is Z(H, T)=Σ__<S_1>Σ__<S_2>・・・Σ__<S_N>e^<-<E{S_i}>/<K_BT>>=e^<<1/k_BT>N(1/2γε-βH)>Σ^^N_<N_+>e^<-2・1/<k_BT>(εγ-βH)N_+>Σ^1__<N_++>g(N_+,N_++)e^<4・1/<K_BT>εN_++>. Next the Ising model can be made to simulate the system of a lattice gas and a binary alloy of other than a ferromagnetic substance by a change of names.