The Blume-Emery-Griffiths model with a random crystal field is studied in a random graph architecture, in which the average connectivity is a controllable parameter. The disordered average over the graph realizations is treated by replica symmetry formalism of order parameter functions. A self-consistent equation for the distribution of local fields is derived and numerically solved by a population dynamics algorithm. The results show that the average connectivity amounts to changes in the topology of the phase diagrams. Phase diagrams for representative values of the model parameters are compared with those obtained for fully connected mean field and renormalization group approaches.
Serial vs parallel recall in the Blume-Every-Griffiths neural networks
Istituto Nazionale di Alta Matematica Francesco Severi（意大利高等数学研究所弗朗切斯科·塞韦里）；Università del Salento（萨伦托大学）；Dipartimento di Matematica e Fisica, Università del Salento（萨伦托大学数学与物理系）；Istituto Nazionale di Fisica Nucleare, Sezione di Lecce（意大利国家核物理研究院莱切分部）；Dipartimento di Informatica, Università di Pisa（比萨大学计算机科学系）；Sapienza Università di Roma（罗马智慧大学）；Dipartimento di Scienze di Base e Applicazioni all’Ingegneria, Sapienza Università di Roma（罗马智慧大学基础科学与工程应用科学系）；Istituto Nazionale di Fisica Nucleare, Sezione di Roma（意大利国家核物理研究院罗马分部）；CNR Nanotec, Sezione di Lecce（意大利国家研究委员会纳米技术研究所莱切分部）
我们分析了具有无序磁相互作用的Blume-Emery-Griffiths模型，该模型表现出逆冻结现象。该自旋1模型在晶体场的行为进行了研究，在整个相图和过渡和spinodal线的模型计算使用全复本对称性破缺Ancroplant，总是产生一个稳定的相位。我们将结果与格子气上具有Ising自旋的淬火无序模型（其中没有再进入发生）以及Schupper和Shnerb最近引入的具有广义自旋变量的模型[Phys. Rev. Lett. 93，037202（2004）]。所有这些模型中最简单的一个版本，称为Ghatak-Sherrington模型，它包含了所有表征向非晶相逆转变的一般特征，包括正确的热力学行为。
