Journal of Magnetism and Magnetic Materials 264 (2003) 175–182 The one-dimensional frustrated Heisenberg antiferromagnet P.A. Leboeuf, M.E. Gouv # ea*, A.S.T. Pires Departamento de F! ısica, ICEx, Universidad Federal de Minas Gerais, Fisica Av. Antonio Carlos 6627-CP 702, 3012 3970, Belo Horizonte MG, Brazil Received 21 November 2002; received in revised form 13 February 2003 Abstract The one-dimensional S ¼ 1=2 antiferromagnetic Heisenberg model with nearest- (J 1 ) and next-nearest-neighbor (J 2 ) interactions is investigated, over the whole temperature region, by employing the double-time Green function method and performing a decoupling proposed by Kondo and Yamaji for cases without long-range order. The susceptibility is calculated and compared to other numerical calculations existing in the literature. We also evaluate the critical value for the J 2 =J 1 ratio and find good agreement with other theoretical estimates. r 2003 Elsevier Science B.V. All rights reserved. PACS: 75.50; 75.10 Keywords: Antiferromagnetic; One-dimensional; Frustration; Long-range interactions 1. Introduction Low-dimensional quantum models have, for many years, been the subject of considerable research, analytical as well as experimental, due to both, the unconventional physics of these models, and the quantum field theoretical methods used in the analysis of the problem [1]. In particular, a great deal of attention has been devoted to the study of spin models that can lead to a better understanding on the behavior of compounds like SrCu 2 O 3 ; VO 2 P 2 O 7 ; and CuGeO 3 where a spin gap occurs. The theoretical work accumulated in the last decades has shown that several mechanisms can be responsible for creating a gap in the energy spectrum, including, for example, competing interactions and quantum fluctuations. As a result, different one-dimensional (1D) quantum antiferromagnetic models have been proposed in order to allow the study of these effects—isolately or not. The properties of quantum systems are known to be strongly affected by fluctuations that can, for example, drive a 1D Heisenberg antiferromagnet with only nearest neighbor (nn) interactions to a lattice dimerization characterizing a Spin-Peierls transition [2,3]. On the other hand, it has been shown that magnetic dimerization can also be induced—even in the absence of lattice dimerization—in 1D systems by the so-called frustration effect involving competing interactions [4,5]. Experimental investigations realized on quasi-1D materials have provided crucial support for the ARTICLE IN PRESS *Corresponding author. Tel.: +553134995669; fax: +553134995600. E-mail address: meg@fisica.ufmg.br (M.E. Gouv# ea). 0304-8853/03/$ - see front matter r 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0304-8853(03)00198-7