Off-Diagonal Long-Range Order in Little's Model

Various authors have shown, using nonrigorous arguments, that the one-dimensional model of Little cannot exhibit off-diagonal long-range order (ODLRO) at nonzero temperatures. Hohenberg has oroven that ODLRO cannot exist at nonzero temperatures in any one-or two-dimensional homogeneous system. Bychkov et al. have shown that the nonhomogeneity in the Little model may produce peculiar forms of ODLRO. Using Bogoliubov's inequality, we prove that such ODLRO vanishes at nonzero temperatures.