发表机构
Institute of Physics, University of Oldenburg; Sorbonne Université（奥尔登堡大学物理研究所; 索邦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究验证了SWAP系综在二维伊辛自旋玻璃中通过缓慢退火可高概率获得基态，并发现较大长度尺度导致铁磁转变，较小尺度保持玻璃态但退火困难。
AI 中文摘要
我们研究了最近提出的用于伊辛自旋玻璃的SWAP系综，其中自旋具有可变长度，长度尺度为$\Delta \in [0, 2]$。这些长度可以按照玻璃态多分散硬球系统的SWAP算法精神进行交换。采用退火调度，如果退火足够缓慢，则可以高概率获得相应伊辛哈密顿量的基态，其中自旋长度被并入键中。我们通过将二维系统（尺寸高达$L^2=1024^2$个自旋）与使用图匹配算法获得的精确基态进行比较，证明了这一论断。特别地，我们通过使用周期性和反周期性边界条件的精确基态计算，计算精确的零温畴壁能量，分析了所获得的无序实现的性质。对于中等或较大的$\Delta$值（例如$\Delta=1$），如果退火足够缓慢，这些实现会转变为铁磁态，即它们失去零温自旋玻璃性质。如果$\Delta$较小，这些实现保持玻璃态，但SWAP退火不容易找到真正的基态。
英文摘要
We study the recently introduced SWAP ensemble for Ising spin-glasses, where the spins obtain varying lengths, with length scale $Δ\in [0, 2]$. The lengths can be exchanged in the spirit of the SWAP algorithm for glassy poly-disperse hard-sphere systems. Using an annealing schedule, if the annealing is slow enough, ground states of the corresponding Ising Hamiltonian, where the spin lengths are incorporated into the bonds, can be obtained with high probability. We prove this statement for two-dimensional systems with sizes of up to $L^2=1024^2$ spins by comparison with exact ground states obtained by using graph matching algorithms. In particular, we analyze the nature of the obtained realizations of the disorder by calculating exact zero-temperature domain-wall energies, from exact ground state calculations using periodic and anti-periodic boundary conditions. For medium or large values of $Δ$, e.g. $Δ=1$, the realizations turn ferromagnetic if the annealing is slow enough, i.e., they lose their zero-temperature spin-glass property. If $Δ$ is small, the realizations remain glassy, but the SWAP annealing does not easily find a true ground state.
Comments19 pages, 19 figures
