近日，西班牙马德里康普顿斯大学的Isidoro González-Adalid Pemartín及其研究小组与意大利罗马大学的Giorgio Parisi等人合作并取得一项新进展。经过不懈努力，他们揭示自旋玻璃中的多重分形行为。相关研究成果已于2024年1月4日在国际知名学术期刊《美国科学院院刊》上发表。

该研究团队揭示了伊辛自旋玻璃在低温相的多重分形行为。研究人员利用Janus II定制超级计算机，局部研究了自旋玻璃相关函数。当对距离相同的两个地点进行比较时，会发现剧烈的波动。研究人员通过计算奇异谱及其相应的勒让德变换，来表征自旋玻璃相干长度随时间增长时这些波动的尺度。

相对较少的位点对控制着对磁场响应的平均相关性。研究人员解释了在小尺度（长度尺度小于相干长度）上存在的剧烈波动，与长期以来被认为描述自旋玻璃动力学的平滑、自平均行为之间的协调关系。

附：英文原文

Title: Multifractality in spin glasses

Author: Baity-Jesi, Marco, Calore, Enrico, Cruz, Andrés, Fernández, Luis Antonio, Gil-Narvión, José Miguel, González-Adalid Pemartín, Isidoro, Gordillo-Guerrero, Antonio, íiguez, David, Maiorano, Andrea, Marinari, Enzo, Martín-Mayor, Víctor, Moreno-Gordo, Javier, Muoz Sudupe, Antonio, Navarro, Denis, Paga, Ilaria, Parisi, Giorgio, Pérez-Gaviro, Sergio, Ricci-Tersenghi, Federico, Ruiz-Lorenzo, Juan Jesús, Schifano, Sebastiano Fabio, Seoane, Beatriz, Tarancón, Alfonso, Yllanes, David

Issue&Volume: 2024-1-4

Abstract: We unveil the multifractal behavior of Ising spin glasses in their low-temperature phase. Using the Janus II custom-built supercomputer, the spin-glass correlation function is studied locally. Dramatic fluctuations are found when pairs of sites at the same distance are compared. The scaling of these fluctuations, as the spin-glass coherence length grows with time, is characterized through the computation of the singularity spectrum and its corresponding Legendre transform. A comparatively small number of site pairs controls the average correlation that governs the response to a magnetic field. We explain how this scenario of dramatic fluctuations (at length scales smaller than the coherence length) can be reconciled with the smooth, self-averaging behavior that has long been considered to describe spin-glass dynamics.

DOI: 10.1073/pnas.2312880120

Source: https://www.pnas.org/doi/abs/10.1073/pnas.2312880120