The random bond-dilution effects of bilinear interaction parameter Jij between the nearest-neighbor (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 order-parameters, 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.

中文翻译：

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键稀释的 Spin-1 Blume-Emery-Griffiths 模型中的交错四极相

对于由两个互穿等效物组成的 Bethe 晶格 (BL) 上的自旋 1 Blume-Emery-Griffiths (BEG) 模型，考虑了最近邻 (NN) 位点之间双线性相互作用参数 Jij 的随机键稀释效应在精确递归关系 (ERR) 方面，对于给定的配位数 z 的子格 A 和 B。假设 Jij 的双峰分布以概率 p 引入或以 1 - p 闭合。假设 NN 自旋之间的双二次交换相互作用参数 (K) 是常数，并且单离子各向异性参数 (D) 被视为在亚晶格 A 和 B 上等效。参数，相图是在我们的系统参数跨越的可能平面上计算的。发现该模型同时呈现一阶和二阶相变。除了众所周知的铁磁 (F)、顺磁 (P) 和亚铁磁 (FI) 相之外，还观察到交错的四极 (SQ) 相。观察到所有 z 的双临界点 (BCP) 和 z ≥ 4 的双 BCP。对于 z ≥ 5 的较低 p 值，也发现了四临界点。