Erichsen R, Silveira A, Magalhaes S G
Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970 Porto Alegre, RS, Brazil.
Phys Rev E. 2021 Feb;103(2-1):022133. doi: 10.1103/PhysRevE.103.022133.
We investigate thermodynamic phase transitions of the joint presence of spin glass (SG) and random field (RF) using a random graph model that allows us to deal with the quenched disorder. Therefore, the connectivity becomes a controllable parameter in our theory, allowing us to answer what the differences are between this description and the mean-field theory i.e., the fully connected theory. We have considered the random network random field Ising model where the spin exchange interaction as well as the RF are random variables following a Gaussian distribution. The results were found within the replica symmetric (RS) approximation, whose stability is obtained using the two-replica method. This also puts our work in the context of a broader discussion, which is the RS stability as a function of the connectivity. In particular, our results show that for small connectivity there is a region at zero temperature where the RS solution remains stable above a given value of the magnetic field no matter the strength of RF. Consequently, our results show important differences with the crossover between the RF and SG regimes predicted by the fully connected theory.
我们使用一个随机图模型来研究自旋玻璃（SG）和随机场（RF）共同存在时的热力学相变，该模型使我们能够处理淬火无序。因此，连通性成为我们理论中的一个可控参数，使我们能够回答这种描述与平均场理论（即完全连通理论）之间的差异是什么。我们考虑了随机网络随机场伊辛模型，其中自旋交换相互作用以及随机场是遵循高斯分布的随机变量。结果是在 replica 对称（RS）近似下得到的，其稳定性是使用双 replica 方法获得的。这也将我们的工作置于更广泛的讨论背景下，即 RS 稳定性作为连通性的函数。特别是，我们的结果表明，对于小连通性，在零温度下存在一个区域，无论随机场的强度如何，在给定磁场值以上 RS 解都保持稳定。因此，我们的结果显示出与完全连通理论预测的随机场和自旋玻璃区域之间的交叉存在重要差异。
