谢灵顿-克里克帕特里克旋转玻璃的经典化使用苏苏基-库博平均场Ising动力学
Soumyaditya Das1, Soumyajyoti Biswas1,2, Bikas K Chakrabarti3
1SRM University-AP, Department of Physics, Amaravati, Andhra Pradesh 522240, India.
Physical review. E
|August 19, 2025
概括
本研究介绍了Sherrington-Kirkpatrick (SK) 旋转玻璃模型的快速经典回火方法. 高效的协议准确地估计了SK模型的基态能量,即使对于大型系统.
科学领域:
- 统计力学 统计力学
- 凝聚物质物理学 凝聚物质物理学
- 计算物理 计算物理
背景情况:
- 谢林顿-基克帕特里克 (SK) 模型是理解旋转眼镜的一个基本模型,其特点是复杂的挫败相互作用.
- 找出SK模型的基本状态能量是由于其NP-hard性质而具有计算挑战.
- 经典的回火方法通常用于找到低能量的状态,但效率可能是一个限制.
研究的目的:
- 开发和数值证明SK旋转玻璃模型的快速经典回火方案.
- 为了高效地估计SK模型的地面状态能量.
- 为了分析能量偏差,波动和回火时间与系统大小的缩放行为.
主要方法:
- 使用苏苏基-库博平均场Ising动力学,并补充了修改后的Thouless-Anderson-Palmer反应场.
- 实施一个快速的经典退火方案,从任意的偏磁阶段开始.
- 数字模拟SK模型的系统大小高达N=10,000次旋转.
主要成果:
- 拟议的动力学很快引导系统到具有小局部磁化的低能配置.
- 能量偏差与基本状态尺度为N^{-2/3},表明在热力学极限中与真正的基本状态能量趋同.
- 能量波动减少为~N^{-3/4},并且火时间尺度与系统大小 (τ_{N}∼N) 线性.
结论:
- 开发的经典回火协议对于估计SK旋转玻璃模型的地面状态能量非常有效.
- 该方法展示了解决统计物理学中复杂的优化问题的实用方法.
- 扩展特性表明该协议对于大规模模拟和精确的能量估计的有效性.
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