(2+1)维gonihedric模型的多重性：A 关于（d,m)=(3,2)Lif*****z点的实现

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摘要翻译：
对2+1维gonihedric模型的多重性进行了数值研究。gonihedric模型是一个完全受挫的伊辛磁体，具有精细调谐的板状（四体和板状-对角线）相互作用，抵消了畴壁表面张力。由于沿虚时方向的量子力学涨落是简单的铁磁涨落，所以(2+1)维角体模型的临界性应该是各向异性的；也就是说，实空间扇区(\perp)和虚时间扇区(\parallel）各自的临界指数并不重合。扩展参数空间控制畴壁表面张力，利用交叉（多层）标度理论分析临界性。通过对n\le28自旋团簇的数值对角化，我们得到了相关长度临界指数(\nu\perp,\nu\paralle)=(0.45(10),1.04(27))和交叉指数phi=0.7(2)。对于（d,m)=(3,2)Lifshitz点，我们的结果与Diehl和Shpot用ε-展开方法得到的(\nu_{\perp},\nu_{\parallel}）=(0.482,1.230)和\phi=0.688相当，直到O(\epsilon^2)。
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英文标题：
《Multicriticality of the (2+1)-dimensional gonihedric model: A
  realization of the (d,m)=(3,2) Lifshitz point》
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作者：
Yoshihiro Nishiyama (Okayama University)
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最新提交年份：
2007
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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：
  Multicriticality of the gonihedric model in 2+1 dimensions is investigated numerically. The gonihedric model is a fully frustrated Ising magnet with the finely tuned plaquette-type (four-body and plaquette-diagonal) interactions, which cancel out the domain-wall surface tension. Because the quantum-mechanical fluctuation along the imaginary-time direction is simply ferromagnetic, the criticality of the (2+1)-dimensional gonihedric model should be an anisotropic one; that is, the respective critical indices of real-space (\perp) and imaginary-time (\parallel) sectors do not coincide. Extending the parameter space to control the domain-wall surface tension, we analyze the criticality in terms of the crossover (multicritical) scaling theory. By means of the numerical diagonalization for the clusters with N\le 28 spins, we obtained the correlation-length critical indices (\nu_\perp,\nu_\parallel)=(0.45(10),1.04(27)), and the crossover exponent \phi=0.7(2). Our results are comparable to (\nu_{\perp},\nu_{\parallel})=(0.482,1.230), and \phi=0.688 obtained by Diehl and Shpot for the (d,m)=(3,2) Lifshitz point with the \epsilon-expansion method up to O(\epsilon^2).
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PDF链接：
https://arxiv.org/pdf/704.3865

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关键词：DRI nih 多重性 interactions Dimensional 扇区 dimensional 研究 对角线 tension