One- and two-dimensional spin systems in the regime close to deconfinement of spinons

Based on the Majumdar-Ghosh chain we construct several spin models which allow us to investigate spinon dynamics in the regime close to deconfinement of spinons. We consider the J1-J2-? model, two coupled J1-J2 chains (ladder), and a two-dimensional array of coupled J1-J2 chains. Using the picture of two spinons interacting with a string confining potential we calculate the singlet-triplet splitting, magnetic structure factor, tunneling amplitude of two spinons, and the excitation spectra for the ladder and the array.