Self-Repelling Elastic Manifolds with Low Dimensional Range

C. Mueller, E. Neuman
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引用次数: 1

Abstract

We consider self-repelling elastic manifolds with a domain $[-N,N]^d \cap \mathbb{Z}^d$, that take values in $\mathbb{R}^D$. Our main result states that when the dimension of the domain is $d=2$ and the dimension of the range is $D=1$, the effective radius $R_N$ of the manifold is approximately $N^{4/3}$. This verifies the conjecture of Kantor, Kardar and Nelson [7]. Our results for the case where $d \geq 3$ and $D
低维范围自排斥弹性流形
我们考虑具有$[-N,N]^d \cap \mathbb{Z}^d$域的自排斥弹性流形,其取值为$\mathbb{R}^D$。我们的主要结果表明,当域的维数为$d=2$,范围的维数为$D=1$时,流形的有效半径$R_N$近似为$N^{4/3}$。这证实了Kantor、Kardar和Nelson[7]的猜想。对于$d \geq 3$和$D
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