Kim Do-Hyun
Jesuit Community, Sogang University, 35 Baekbeom-ro, Mapo-gu, Seoul 121-742, Korea.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Feb;89(2):022803. doi: 10.1103/PhysRevE.89.022803. Epub 2014 Feb 10.
In this paper, we will investigate critical phenomena by considering a model spin glass on scale-free networks. For this purpose, we consider the Ghatak-Sherrington (GS) model, a spin-1 spin-glass model with a crystal field, instead of the usual Ising-type model. Scale-free networks on which the GS model is placed are constructed from the static model, in which the number of vertices is fixed from the beginning. On the basis of the replica-symmetric solution, we obtain the analytical solutions, i.e., free energy and order parameters, and we derive the various phase diagrams consisting of the paramagnetic, ferromagnetic, and spin-glass phases as functions of temperature T, the degree exponent λ, the mean degree K, and the fraction of the ferromagnetic interactions ρ. Since the present model is based on the GS model, which considers the three states (S = 0, ± 1), the S = 0 state plays a crucial role in the λ-dependent critical behavior: glass transition temperature T(g) has a finite value, even when 2 < λ < 3. In addition, when the crystal field becomes nonzero, the present model clearly exhibits three types of inverse transitions, which occur when an ordered phase is more entropic than a disordered one.
在本文中，我们将通过考虑无标度网络上的一个模型自旋玻璃来研究临界现象。为此，我们考虑加塔克 - 谢林顿（GS）模型，一个具有晶体场的自旋 - 1自旋玻璃模型，而不是通常的伊辛型模型。放置GS模型的无标度网络是由静态模型构建的，其中顶点数量从一开始就固定。基于 replica - symmetric 解，我们得到解析解，即自由能和序参量，并推导由顺磁、铁磁和自旋玻璃相组成的各种相图，这些相图是温度T、度指数λ、平均度K和铁磁相互作用分数ρ的函数。由于当前模型基于GS模型，该模型考虑了三种状态（S = 0, ± 1），S = 0状态在依赖于λ的临界行为中起着关键作用：即使当2 < λ < 3时，玻璃化转变温度T(g)也有一个有限值。此外，当晶体场变为非零时，当前模型清楚地展示出三种类型的逆转变，这些逆转变发生在有序相比无序相具有更高熵的时候。
