Solvable models of spin-1/2 chains with an energy gap

An XY model with two kinds of coupling constants J and -K is investigated. The system has plural spin sites in a unit cell, where the coupling constant inside a unit cell is -K, and the coupling constant between two unit cells is J. When the number of the spin sites L in a unit cell is even (or odd), there is an energy gap (or no gap) between the ground state and the first excited state (for ‖K/J‖≠1). The magnetization of the system with any even number of L vanishes below a critical magnetic field at the temperature T=0. Therefore, the susceptibility is zero at T=0 when L is even, but the susceptibility is positive when L is odd. The data for the magnetization of (${\mathrm{CH}}_3$ ${)}_4$N Ni (${\mathrm{NO}}_2$ ${)}_3$ resemble the calculated value of the magnetization for L=2. © 1996 The American Physical Society.