Substrate effects on long-range order and scattering from low-dimensional systems

Using solvable models it is shown that coupling one- and two-dimensional systems to substrates produces significant alterations in their long-range order and scattering characteristics, even if the coupling is very weak. Expressions for Peierls's long-range-order parameter, 〈₍^2〉, are obtained, with their asymptotic forms, and static structure factors, S (Q), are evaluated.