Decay of Order in Isotropic Systems of Restricted Dimensionality. I. Bose Superfluids

Abstract

The off-diagonal ordering of one- and two-dimensional Bose particle systems of finite thickness and cross-section is considered in the presence and absence of a symmetry-breaking field. It is shown rigorously, by applying Bogoliubov's inequality to a subdomain of the system, that no spontaneous ordering can occur; several definitions of long-range order are discussed. Explicit bounds on the order-order correlation function, integrated over a subdomain, are obtained which indicate how the short-range order decays with distance. Conditions under which information on the pointwise behavior of the correlation function can be inferred are also discussed. The inequalities are assessed numerically for real situations.