Generalization of Mean-Field Approximations by the Feynman Inequality and Application to Long-Range Ising Chain
Minoru Takahashi · Journal of the Physical Society of Japan · 1981
Mean-field approximations such as molecular field approximation for spin system, Hartree-Fock approximation and BCS approximation for electron system are universally formulated by the Feynman inequality: -β -1 ln Tr exp (-β H ) ≤-β -1 ln Tr exp (-β H 0 )+Tr exp (-β H 0 )( H - H 0 )/Tr exp (-β H 0 ). The method of generalization of mean-field approximation is given. This is applied to the problem of one-dimensional long-range Ising model.