论文标题
在零温度下随机图上的Ising自旋玻璃：并非所有旋转都是玻璃相的玻璃
The Ising spin glass on random graphs at zero temperature: not all spins are glassy in the glassy phase
论文作者
论文摘要
我们研究了在零温度下定义的伯特晶格上定义的随机场中自旋玻璃（SG）模型的复制对称性（RSB）相。从RSB解决方案的属性中，我们推导了一个腔场极端值的封闭方程。事实证明，该方程式不取决于定义RSB的参数，并且预测自发的RSB不会在整个系统上同质发生。实际上，在所有局部接地状态下，存在与复制品对称（RS）相相同的有效局部领域，而自发的RSB仅在其余的旋转上表现出来，其分数在临界时消失。在具有固定或波动的局部场的旋转方面的表征也可以扩展到随机场Ising模型（RFIM），在这种情况下，波动的旋转是铁磁相中自发磁化的唯一负责。接近临界点，我们能够将作用在RSB阶段上旋转的局部场的统计数据与在顺磁相测量的相关函数联系起来。在给定SG和RFIM的给定实例中，识别两种类型的旋转，我们表明它们的参与与通过翻转单个旋转产生的雪崩截然不同。从接近临界点的旋转数量诱导RSB效应的缩放，并使用$ M $ - 层扩展，我们估计SG的上限临界尺寸$ d_u \ geq 8 $。
We investigate the replica symmetry broken (RSB) phase of spin glass (SG) models in a random field defined on Bethe lattices at zero temperature. From the properties of the RSB solution we deduce a closed equation for the extreme values of the cavity fields. This equation turns out not to depend on the parameters defining the RSB, and it predicts that the spontaneous RSB does not take place homogeneously on the whole system. Indeed, there exist spins having the same effective local field in all local ground states, exactly as in the replica symmetric (RS) phase, while the spontaneous RSB manifests only on the remaining spins, whose fraction vanishes at criticality. The characterization in terms of spins having fixed or fluctuating local fields can be extended also to the random field Ising model (RFIM), in which case the fluctuating spins are the only responsible for the spontaneous magnetization in the ferromagnetic phase. Close to criticality we are able to connect the statistics of the local fields acting on the spins in the RSB phase with the correlation functions measured in the paramagnetic phase. Identifying the two types of spins on given instances of SG and RFIM, we show that they participate very differently to avalanches produced by flipping a single spin. From the scaling of the number of spins inducing RSB effects close to the critical point and using the $M$-layer expansion we estimate the upper critical dimension $D_U \geq 8$ for SG.
