Staggered Quadrupolar Phase in the Bond-Diluted Spin-1 Blume-Emery-Griffiths Model
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Staggered Quadrupolar Phase in the Bond-Diluted Spin-1 Blume-Emery-Griffiths Model J. Kple1,2 · F. Hontinfinde1,2 · E. Albayrak3 Received: 1 June 2020 / Accepted: 23 October 2020 / © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The random bond-dilution effects of bilinear interaction parameter Jij between the nearestneighbor (NN) sites are taken into consideration for the spin-1 Blume-Emery-Griffiths (BEG) model on the Bethe lattice (BL) comprised of two interpenetrating equivalent sublattices A and B for given coordination number z in terms of exact recursion relations (ERR). A bimodal distribution for Jij is assumed which is either introduced with probability p or closed with 1 − p. It is assumed that the biquadratic exchange interaction parameter (K) is constant between the NN spins and the single-ion anisotropy parameter (D) is taken to be equivalent on the sublattices A and B. After the study of thermal changes of the orderparameters, the phase diagrams are calculated on possible planes spanned by our system parameters. It is found that the model presents both first- and second-order phase transitions. In addition to the well-known ferromagnetic (F), paramagnetic (P) and ferrimagnetic (FI) phases, the staggered quadrupolar (SQ) phase is also observed. The bicritical point (BCP) for all z and double BCP with z ≥ 4 are observed. The tetracritical point was also found for lower values of p with z ≥ 5. Keywords Spin-1 · Randomness · BEG model · Staggered quadrupole phase · Bimodal · Bethe lattice
1 Introduction The BEG model Hamiltonian consists of bilinear and biquadratic exchange interaction parameters in addition to the crystal field term. Since the spin-1 model is the lowest model consisting of all these parameters, it was thoroughly investigated by using numerous techniques. A closed-form expression for the critical surface of second-order transitions was formulated as a three-state vertex model [1]. Dimensionality effects with repulsive K < 0 were examined by using the mean field (MF) and renormalization-group (RG) studies E. Albayrak
[email protected] 1
Institute of Mathematic and Physical Sciences (IMSP), Dangbo, Republic of Benin
2
Department of Physics, University of Abomey-Calavi, Godomey, Republic of Benin
3
Department of Physics, Erciyes University, 38039, Kayseri, Turkey
International Journal of Theoretical Physics
[2] and it was shown that the results obtained by MF theory were applicable to threedimensional systems [3]. The random-anisotropy model was considered by using the MF theory, transfer-matrix calculations and position-space (RG) calculations [4]. It was analyzed by using Monte Carlo (MC) RG study on the cubic lattice with K < 0 [5]. It is proven that BEG model can be transformed into either a spin-l/2 Ising model or a 3-state Potts model [6]. It was studied within the framework of a finite cluster theory on a diamond lattice [7]. The model with transverse D and, the longitudinal and transverse magnetic fields was studied via the MFA [8]. The d
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