Faculty of Engineering and Natural Sciences, Sabancı University, Tuzla, Istanbul 34956, Turkey.
Faculty of Engineering and Natural Sciences, Kadir Has University, Cibali, Istanbul 34083, Turkey.
Phys Rev E. 2018 May;97(5-1):052102. doi: 10.1103/PhysRevE.97.052102.
Discrete-spin systems with maximally random nearest-neighbor interactions that can be symmetric or asymmetric, ferromagnetic or antiferromagnetic, including off-diagonal disorder, are studied, for the number of states q=3,4 in d dimensions. We use renormalization-group theory that is exact for hierarchical lattices and approximate (Migdal-Kadanoff) for hypercubic lattices. For all d>1 and all noninfinite temperatures, the system eventually renormalizes to a random single state, thus signaling q×q degenerate ordering. Note that this is the maximally degenerate ordering. For high-temperature initial conditions, the system crosses over to this highly degenerate ordering only after spending many renormalization-group iterations near the disordered (infinite-temperature) fixed point. Thus, a temperature range of short-range disorder in the presence of long-range order is identified, as previously seen in underfrustrated Ising spin-glass systems. The entropy is calculated for all temperatures, behaves similarly for ferromagnetic and antiferromagnetic interactions, and shows a derivative maximum at the short-range disordering temperature. With a sharp immediate contrast of infinitesimally higher dimension 1+ε, the system is as expected disordered at all temperatures for d=1.
我们研究了具有最大随机近邻相互作用的离散自旋系统，这些系统可以是对称的或不对称的，铁磁的或反铁磁的，包括非对角无序，状态数量 q=3,4 在 d 维。我们使用重整化群理论，对于层次晶格是精确的，对于超立方晶格是近似的（Migdal-Kadanoff）。对于所有 d>1 和所有非无穷大温度，系统最终都会重整化到一个随机的单一状态，从而表明 q×q 简并有序。请注意，这是最大简并有序。对于高温初始条件，系统仅在经过许多重整化群迭代接近无序（无穷大温度）固定点后，才会跨越到这种高度简并的有序状态。因此，在存在长程有序的情况下，确定了短程无序的温度范围，如以前在欠挫折的伊辛自旋玻璃系统中看到的那样。我们计算了所有温度下的熵，铁磁和反铁磁相互作用的行为相似，并在短程无序温度处显示出导数最大值。在尺寸 ε 的无限小增量的急剧对比下，正如预期的那样，对于 d=1，系统在所有温度下都是无序的。
