One-dimensional free-electron spin susceptibility at finite temperature

Abstract

The analytical expression of the free-electron spin susceptibilities chi(q) and chi(r) in one dimension are derived at finite temperature, where the Sommerfeld expansion is not applicable near q=2k(F), by a series expansion method which does not require the restriction of the Sommerfeld method. The main results are (i) the oscillation of the range function decays exponentially as exp(-pi k(F)rk(B)T/epsilon(F)) in the long-range limit and (ii) the logarithmic divergence of chi(q) at q=2k(F) near T=0 is in the form of [N(0)mu(B)(2)/2]ln(4 epsilon(F)/pi k(B)T).