Generalization of Mean-Field Approximations by the Feynman Inequality and Application to Long-Range Ising Chain

抄録

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 (−βH)≤−β⁻¹ ln Tr exp (−βH₀)+Tr exp (−βH₀)(H−H₀)⁄Tr exp (−βH₀). The method of generalization of mean-field approximation is given. This is applied to the problem of one-dimensional long-range Ising model.