Random isotropic one-dimensional XY-model

• Published in: Journal of magnetism and magnetic materials Vol. 177; pp. 79 - 80
• Main Authors: Gonçalves, L.L., Vieira, A.P.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 1998
• Subjects: Magnetization — low temperature; One-dimensional systems; Random systems; XY-model; Magnetization — low temperature; Random systems; XY-model; One-dimensional systems
• ISSN: 0304-8853
• DOI: 10.1016/S0304-8853(97)00414-9

The 1D isotropic s = ½XY-model ( N sites), with random exchange interaction in a transverse random field is considered. The random variables satisfy bimodal quenched distributions. The solution is obtained by using the Jordan-Wigner fermionization and a canonical transformation, reducing the problem to diagonalizing an N × N matrix, corresponding to a system of N noninteracting fermions. The calculations are performed numerically for N = 1000, and the field-induced magnetization at T = 0 is obtained by averaging the results for the different samples. For the dilute case, in the uniform field limit, the magnetization exhibits various discontinuities, which are the consequence of the existence of disconnected finite clusters distributed along the chain. Also in this limit, for finite exchange constants J A and J B , as the probability of J A varies from one to zero, the saturation field is seen to vary from Γ A to Γ B , where Γ A(Γ B) is the value of the saturation field for the pure case with exchange constant equal to J A(J B) .