关于有效场论在预测Ising纳米粒子、纳米岛、纳米管和纳米线的伪自发有序和相变中的失败
On the failure of effective-field theory in predicting a spurious spontaneous ordering and phase transition of Ising nanoparticles, nanoislands, nanotubes and nanowires
摘要：
目前的工作澄清了失败的有效场论在预测一个错误的自发长程序和相变的伊辛纳米粒子，纳米岛，纳米管和纳米线的零维或一维的磁性维度。本文指出，Honmura和Kaneyoshi的有效场论的标准公式一般预言，只要至少有一个Ising自旋的配位数大于2，Ising自旋系统就会出现一个非零临界温度的伪自发长程序，而与它们的磁维数无关。有效场论的失败可以用几个零维和一维伊辛纳米系统的精确解的例子来说明：星形、立方体、装饰六边形、大卫之星、支链、双链、两条腿和六角梯子。给出的精确解说明了几种严格的分析方法对Ising纳米系统的精确处理的适用性：精确计数法、图论方法、转移矩阵法和装饰迭代变换。本文还提供了大量的科学文献，其中有效场论导致了一个错误的预测的自发长程有序和相变的调查。
英文摘要：
The present work clarifies a failure of the effective-field theory in predicting a false spontaneous long-range order and phase transition of Ising nanoparticles, nanoislands, nanotubes and nanowires with either zero- or one-dimensional magnetic dimensionality. It is conjectured that the standard formulation of the effective-field theory due to Honmura and Kaneyoshi generally predicts for the Ising spin systems a spurious spontaneous long-range order with nonzero critical temperature regardless of their magnetic dimensionality whenever at least one Ising spin has coordination number greater than two. The failure of the effective-field theory is exemplified on a few paradigmatic exactly solved examples of zero- and one-dimensional Ising nanosystems: star, cube, decorated hexagon, star of David, branched chain, sawtooth chain, two-leg and hexagonal ladders. The presented exact solutions illustrate eligibility of a few rigorous analytical methods for exact treatment of the Ising nanosystems: exact enumeration, graph-theoretical approach, transfer-matrix method and decoration-iteration transformation. The paper also provides a substantial survey of the scientific literature, in which the effective-field theory led to a false prediction of the spontaneous long-range ordering and phase transition.
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