Lagrangian theory for a self-avoiding random chain

Publisher Website

1 November 1974

journal article
research article
Published by American Physical Society (APS) in Physical Review A

Vol. 10 (5) , 1665-1669
https://doi.org/10.1103/physreva.10.1665

Abstract

The Lagrangian theory of random chains with excluded volume is used to study

Z_{N} (\vec{r})

, the number of chains with

N

links, starting from the origin and arriving at a point

\vec{r}

. Its asymptotic expression (

N \to \infty

) is

Z_{N} (r) ≃ N^{γ - 1 - ν d} F (r N^{- ν})

, where

γ

and

ν

are critical indices. The short- and long-range behaviors of

F (x)

are calculated in terms of

γ

and

ν

. In particular, it is shown that for

x ≪ 1

, we have

F (x) ≃ F x^{θ}

with

F = const

and

θ = \frac{(γ - 1)}{ν}

.

Keywords

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