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

Based on the Majumdar-Ghosh chain we construct several spin models which al low us to investigate spinon dynamics in the regime close to deconfinement of spinons. We consider the J(1)-J(2)-delta model, two coupled J(1)-J(2) ch ains (ladder), and a two-dimensional array of coupled J(1)-J(2) chains. Usi ng the picture of two spinons interacting with a string confining potential we calculate the::singiet-triplet splitting, magnetic structure factor tun neling amplitude of two spinons, and the excitation spectra for the ladder and the array. [S0163-1829(99)05329-1].