Theoretical study of Cu-O chain fragments in the oxygen-deficient planes of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6+\mathit{x}}$. II. Intrachain interactions and the chain fragment’s length distribution

We study some models of the strongly correlated ⋅⋅⋅Cu-O⋅⋅⋅ chain fragments that form on the oxygen-deficient planes of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6+\mathit{x}}$. We use analytical and numerical methods to investigate the stability of the chain fragments as a function of their size. We discuss also the size and x dependence of the O-O intrachain interactions that enter in the phenomenological descriptions of the ${\mathrm{CuO}}_{\mathit{x}}$ planes. Only the fermionic degrees of freedom of the chain fragments are considered. © 1996 The American Physical Society.