Physica A 349 (2005) 471–486 The critical behavior of the mixed spin-1 and spin-2 Ising ferromagnetic system on the Bethe lattice Erhan Albayrak à , Ali Yigit Department of Physics, Erciyes University, 38039 Kayseri, Turkey Received 19 August 2004 Available online 23 November 2004 Abstract The phase diagrams of the mixed spin-1 and spin-2 Blume–Capel Ising ferromagnetic system ðJ 40Þ with two crystal-field interactions, D A for spin-1 and D B for spin-2, is studied on the Bethe lattice by using the exact recursion equations. The exact expressions of the order- parameters for the sublattices with spin-1 and spin-2, and the Curie temperature and the free energy of the system are obtained in terms of the recursion relations. The phase diagrams on the ðkT c =J ; D A =J Þ and ðkT c =J ; D B =J Þ planes are studied for selected values of D B =J and D A =J ; respectively, for the coordination numbers q ¼ 3; 4; and 6. Besides the second-order phase transition lines, the lines of the first-order phase transitions terminating either at a tricritical point or at an isolated critical point are found. r 2004 Elsevier B.V. All rights reserved. PACS: 05.50.+q; 05.70.Fh; 64.60.Cn; 75.10.Hk Keywords: Mixed spin; Bethe lattice; Exact recursion equations ARTICLE IN PRESS www.elsevier.com/locate/physa 0378-4371/$-see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physa.2004.10.036 à Corresponding author. E-mail address: albayrak@erciyes.edu.tr (E. Albayrak).