Hyperscaling above the upper critical dimension
Hyperscaling above the upper critical dimension
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DOI：
10.1016/j.nuclphysb.2012.07.021
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发表时间：
2012-12-01
影响因子：
2.8
通讯作者：
Walter, J. -C.
中科院分区：
文献类型：
--
作者：
Berche, B.;Kenna, R.;Walter, J. -C.
在上临界维度以上，超标度的破裂与重整化群形式中危险的无关变量有关，至少对于具有周期边界条件的系统是如此。虽然这些已经得到了广泛的研究，但对自由边界条件下的有限尺寸标度的分析还很少。传统的期望是，与周期几何不同，有限大小的标度是高斯的，由与晶格范围相称的关联长度控制。这里，对五维伊辛模型的详细数值研究表明，这种期望是不被支持的：它是无限体积的临界点，也是在有限尺寸磁化率峰值的伪临界点。相反，证据表明，准临界点的有限尺寸标度与周期情况下的标度相似。提供了一种解析解释，允许超标度扩展到超过上临界维度。(C)2012爱思唯尔B.V.保留所有权利。
Above the upper critical dimension, the breakdown of hyperscaling is associated with dangerous irrelevant variables in the renormalization group formalism at least for systems with periodic boundary conditions. While these have been extensively studied, there have been only a few analyses of finite-size scaling with free boundary conditions. The conventional expectation there is that, in contrast to periodic geometries, finite-size scaling is Gaussian, governed by a correlation length commensurate with the lattice extent. Here, detailed numerical studies of the five-dimensional Ising model indicate that this expectation is unsupported, both :it the infinite-volume critical point and at the pseudocritical point where the finite-size susceptibility peaks. Instead the evidence indicates that finite-size scaling at the pseudocritical point is similar to that in the periodic case. An analytic explanation is offered which allows hyperscaling to be extended beyond the upper critical dimension. (C) 2012 Elsevier B.V. All rights reserved.