摘要翻译：
本文研究了空间各向异性对具有周期边界条件的O$(n)$对称各向异性$\phi^4$晶格模型体和有限尺寸临界行为的影响。讨论了体序参量相关函数、体散射强度和几种普遍的体振幅关系不存在双尺度因子普适性的问题。对于受限系统，在2<d<4$的定维D$最小减法下，采用重整化群理论。对于立方对称和$n=1$的情况，我们的微扰方法与Monte Carlo(MC)关于三维Ising模型自由能有限尺寸振幅的Monte Carlo(MC)数据非常一致[Phys.Rev.Lett.{\bf 54},2671（1985）]。在$t_c$以下，发现了过量自由能标度函数的一个极小值。我们预测了这个最小值对各向异性参数的可测量依赖性。相对各向异性对自由能的影响明显大于对粘结累积量的影响。我们的理论与Selke和Shchur的MC模拟[J.Phys.{\bf A 38},L739(2005)]发现的Binder累积量对二维Ising模型铁磁次近邻(NNN)耦合的非单调依赖性在定量上一致。我们的理论还预言了{It反铁磁}NNN耦合值较小时的非单调依赖关系，以及在该耦合值较大时的Lifschitz点的存在。在有限尺度范围内，非普适各向异性效应满足一种受限制的普适性。在$t\neqt_c$处的large-$l$行为的尾部违反了有限大小的伸缩和通用性。
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英文标题：
《Diversity of critical behavior within a universality class》
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作者：
Volker Dohm
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最新提交年份：
2008
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
  We study spatial anisotropy effects on the bulk and finite-size critical behavior of the O$(n)$ symmetric anisotropic $\phi^4$ lattice model with periodic boundary conditions in a $d$-dimensional hypercubic geometry above, at and below $T_c$. The absence of two-scale factor universality is discussed for the bulk order-parameter correlation function, the bulk scattering intensity, and for several universal bulk amplitude relations. For the confined system, renormalization-group theory within the minimal subtraction scheme at fixed dimension $d$ for $2<d<4$ is employed. For the case of cubic symmetry and for $n=1$ our perturbation approach yields excellent agreement with the Monte Carlo (MC) data for the finite-size amplitude of the free energy of the three-dimensional Ising model at $T_c$ by Mon [Phys. Rev. Lett. {\bf 54}, 2671 (1985)]. Below $T_c$ a minimum of the scaling function of the excess free energy is found. We predict a measurable dependence of this minimum on the anisotropy parameters. The relative anisotropy effect on the free energy is predicted to be significantly larger than that on the Binder cumulant. Our theory agrees quantitatively with the non-monotonic dependence of the Binder cumulant on the ferromagnetic next-nearest neighbor (NNN) coupling of the two-dimensional Ising model found by MC simulations of Selke and Shchur [J. Phys. {\bf A 38}, L739 (2005)]. Our theory also predicts a non-monotonic dependence for small values of the {\it antiferromagnetic} NNN coupling and the existence of a Lifschitz point at a larger value of this coupling. The nonuniversal anisotropy effects in the finite-size scaling regime are predicted to satisfy a kind of restricted universality. The tails of the large-$L$ behavior at $T \neq T_c$ violate both finite-size scaling and universality.
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PDF链接：
https://arxiv.org/pdf/801.4096