THE CRUMPLING TRANSITION OF CRYSTALLINE RANDOM SURFACES
THE CRUMPLING TRANSITION OF CRYSTALLINE RANDOM SURFACES
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DOI：
10.1016/0550-3213(91)90166-u
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发表时间：
1991-02-25
影响因子：
2.8
通讯作者：
WHEATER, JF
中科院分区：
文献类型：
--
作者：
HARNISH, RG;WHEATER, JF
我们研究了最近引起一些混乱的两种不同模型的具有非本征曲率的晶体随机表面的皱缩相变，发现以前得到的许多结果是错误的。使用傅立叶加速技术来改善临界减速问题，我们对嵌入在三维中的多达128(2)点的表面进行了数值模拟。第一个模型具有非紧凑的格子版本的非本征曲率，在非褶皱相中遭受疾病，这是晶格伪影；它在一个内在方向上是平滑的，而在另一个方向上是在晶格间距的尺度上折叠的，所以我们称之为波纹相。皱缩转变是连续的，有一个发散的持续长度，临界指数v=1.15+/-0.15，在比热中有一个尖点，表明α小于或等于0。第二个模型的外曲率取决于相邻三角形的法线夹角的余弦，它也是连续过渡的，v=0.94+/-0.20，α=0.53+/-0.15。在皱缩相变之后，发现光滑相的Hausdorff维数d(H)<；2.14有两个标准差，因此我们得出结论，在整个相变过程中d(H)=2。对关联函数的研究表明，在皱缩阶段，系统明显地用一个非常简单的高斯作用来描述。如果这是真的，这一结果可能会有重要的影响，我们简要讨论一下。
We investigate the crumpling transition in two different models of crystalline random surfaces with extrinsic curvature which have recently caused some confusion and find that many of the results previously obtained are erroneous. Using the Fourier acceleration technique to ameliorate critical slowing down problems we have made numerical simulations of surfaces of up to 128(2) points embedded in three dimensions. The first model, which has a non-compact lattice version of the extrinsic curvature, suffers from a sickness in the non-crumpled phase which is a lattice artefact; it is smooth in one intrinsic direction and folded up on the scale of the lattice spacing in the other, so we call this phase corrugated. The crumpling transition is continuous, having a diverging persistence length with critical exponent v = 1.15 +/- 0.15 and a cusp in the specific heat indicating that alpha less-than-or-equal-to 0. The second model, in which the extrinsic curvature depends upon the cosine of the angle between normals of adjacent triangles, also has a continuous transition with v = 0.94 +/- 0.20 and alpha = 0.53 +/- 0.15. Just beyond the crumpling transition, the smooth phase is found to have Hausdorff dimension d(H) < 2.14 at two standard deviations and so we conclude that d(H) = 2 throughout this phase. A study of the correlation functions shows that, in the crumpled phase, the system is apparently described by a very simple gaussian action. If true, this result could have important implications which we discuss briefly.