The XY model on the one-dimensional superlattice: static properties

The XY model (s = 1/2) on the one-dimensional alternating superlattice (clo sed chain) is solved exactly by using a generalized Jordan-Wigner transform ation and the Green function method. Closed expressions are obtained for th e excitation spectrum, the internal energy, the specific heat, the average magnetization per site, the static susceptibility, X-zz, and the two-spin c orrelation function in the field direction at arbitrary temperature. At T = 0, it is shown that the system presents multiple second-order phase transi tions induced by the transverse field, which are associated to the zero ene rgy mode with wave number equal to 0 or pi. It is also shown that the avera ge magnetization as a function of the held presents, alternately, regions o f plateaux (disordered phases) and regions of variable magnetization (order ed phases). The static correlation function presents an oscillating behavio r in the ordered phase and its period goes to infinity at the critical poin t. (C) 1999 Elsevier Science B.V. All rights reserved.The XY model (s = 1/2 ) on the one-dimensional alternating superlattice (closed chain) is solved exactly by using a generalized Jordan-Wigner transformation and the Green f unction method. Closed expressions are obtained for the excitation spectrum , the internal energy, the specific heat, the average magnetization per sit e, the static susceptibility, chi(zz), and the two-spin correlation functio n in the field direction at arbitrary temperature. At T = 0, it is shown th at the system presents multiple second-order phase transitions induced by t he transverse field, which are associated to the zero energy mode with wave number equal to 0 or pi. It is also shown that the average magnetization a s a function of the held presents, alternately, regions of plateaux (disord ered phases) and regions of variable magnetization (ordered phases). The st atic correlation function presents an oscillating behavior in the ordered p hase and its period goes to infinity at the critical point. (C) 1999 Elsevi er Science B.V. All rights reserved.