Physica A 389 (2010) 2725–2732 Contents lists available at ScienceDirect Physica A journal homepage: www.elsevier.com/locate/physa Ground state phase diagrams for the mixed Ising 3/2 and 5/2 spin model N. De La Espriella a,b , G.M. Buendía a,∗ a Department of Physics, Universidad Simón Bolívar, Caracas 1080, Venezuela b Department of Physics, Grupo Gamasco, Universidad de Córdoba, Córdoba 230002, Colombia article info Article history: Received 20 January 2010 Received in revised form 1 March 2010 Available online 23 March 2010 Keywords: Mixed Ising models Ground-state phase diagrams abstract We calculate the ground state phase diagrams of a mixed Ising model on a square lattice where spins S (±3/2, ±1/2) in one sublattice are in alternating sites with spins Q (±5/2, ±3/2, ±1/2), located on the other sublattice. The Hamiltonian of the model includes first neighbor interactions between the S and Q spins, next-nearest-neighbor interactions between the S spins, and between the Q spins, and crystal field. The topologies of the phase diagrams depend on the values of the parameters in the Hamiltonian. The diagrams show some key features: coexistence between regions, points where two, three, four, five and six states can coexist. Besides being very useful as a way to check the low temperature limit of the finite-temperature phase diagram, often obtained by mean-field theories, the richness of the ground state diagrams for certain combinations of parameters can be used as a guide to explore interesting regions of the finite-temperature phase diagram of the model. © 2010 Elsevier B.V. All rights reserved. 1. Introduction Mixed Ising systems with higher spins have been actively studied in condensed matter and statistical physics. Their relative simplicity and rich behavior make them an excellent laboratory to study a variety of multicritical phenomena. More recently, these systems have become increasingly relevant for the understanding of novel bimetallic molecular compounds the structure of which resembles two kinds of magnetic atoms alternating in a regular lattice [1–5]. In particular, the less explored mixed spin-3/2 and spin-5/2 model seems to be pertinent to the understanding of certain biological compounds. Numerous experiments indicate that a mix of 3/2 and 5/2 spins is behind the unusual magnetic properties of certain types of ferric heme proteins known as ferricytochromes c’ [6–9]. Besides their crucial role in oxygen transport by blood, heme proteins are used as a synthetic base to design novel biomaterials with potential applications in optical communications, and are considered as the base for nanoporous catalytic materials [10]. As far as we know there have been very few studies on this mixed system, most of them based on mean-field approaches. These mean-field studies suggest that the 3/2–5/2 mixed Ising system has a rich magnetic structure that includes first- and second-order phase transitions, compensation temperatures, and reentrant behavior [11–15]. As a first step toward a deeper understanding of this model, we present a detailed analysis of its ground state behavior when nearest-neighbor, next-nearest-neighbor interactions and crystal field, are present. Ground state phase diagrams are an important tool to understand finite-temperature phase diagrams, to locate critical points, and are very helpful to check the reliability of numerical and theoretical results. In this work we calculate exactly the ground state diagram of a mixed Ising 3/2–5/2 spin model, by enumerating all the possible states of the system in a square lattice and numerically calculating their energy. The remainder of this paper is organized as follows. In Section 2 we introduce the model and explain how the ground state diagrams are calculated. In the subsections therein we present the ground state diagrams for the different combinations of parameters in the Hamiltonian. The conclusions are presented in Section 3. ∗ Corresponding author. Tel.: +58 212 9063556; fax: +58 212 9063600. E-mail address: buendia@usb.ve (G.M. Buendía). 0378-4371/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physa.2010.03.022