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Critical properties of small world Ising models.

机译：小世界伊辛模型的关键属性。

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摘要

In this dissertation, the critical scaling behavior of magnetic Ising models with long range interactions is studied. These long range interactions, when imposed in addition to interactions on a regular lattice, lead to small-world graphs. By using large-scale Monte Carlo simulations, together with finite-size scaling, the critical behavior of a number of different models is obtained. The Ising models studied in this dissertation include the z -model introduced by Scalettar, standard small-world bonds superimposed on a square lattice, and physical small-world bonds superimposed on a square lattice. From the scaling results of the Binder 4th order cumulant, the order parameter, and the susceptibility, the long-range interaction is found to drive the systems behavior from Ising-like to mean field, and drive the critical point to a higher temperature. It is concluded that with a large amount of strong long-range connections (compared to the interactions on regular lattices), so the long-range connection density is non-vanishing, systems have mean field behavior. With a weak interaction that vanishes for an infinite system size or for vanishing density of long-range connections the systems have Ising-like critical behavior. The crossover from Ising-like to mean-field behavior due to weak long-range interactions for systems with a large amount of long-range connections is also discussed. These results provide further evidence to support the existence of physical (quasi-) small-world nanomaterials.
机译：本文研究了具有长程相互作用的电磁伊辛模型的临界尺度行为。除了在规则晶格上进行交互之外，如果将这些远程交互作用强加于它们，也会导致生成小图。通过使用大规模蒙特卡洛模拟以及有限大小的缩放比例，可以获得许多不同模型的临界行为。本文研究的Ising模型包括Scalettar提出的z模型，叠加在方格上的标准小世界键和叠加在方格上的物理小世界键。从Binder四阶累积量的缩放结果，阶数参数和磁化率，可以发现远程相互作用将系统行为从类Ising驱使到均值场，并将临界点驱动到更高的温度。结论是，由于存在大量的强远程连接（与规则晶格上的相互作用相比），因此远程连接密度不消失，系统具有平均场行为。对于较弱的交互作用，该交互作用对于无限的系统大小或远程连接的密度会消失，因此系统具有类似于Ising的临界行为。还讨论了由于具有大量远程连接的系统的弱远程交互作用，从类Ising到平均场行为的转换。这些结果为支持物理（准）小世界纳米材料的存在提供了进一步的证据。

著录项

  • 作者

    Zhang, Xingjun.;

  • 作者单位

    Mississippi State University.;

  • 授予单位 Mississippi State University.;
  • 学科 Physics Condensed Matter.; Engineering Materials Science.
  • 学位 Ph.D.
  • 年度 2005
  • 页码 289 p.
  • 总页数 289
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 工程材料学;
  • 关键词

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