|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'500'096
Articles rated: 2609
19 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Directed Polymers with Random Interaction : An Exactly Solvable Case - | | Sutapa Mukherji
; Somendra M. Bhattacharjee
; | | Date: |
11 Nov 1993 | | Subject: | cond-mat | | Abstract: | We propose a model for two $(d+1)$-dimensional directed polymers subjected to a mutual $delta$-function interaction with a random coupling constant, and present an exact renormalization group study for this system. The exact $eta$-function, evaluated through an $epsilon(=1-d)$ expansion for second and third moments of the partition function, exhibits the marginal relevance of the disorder at $d=1$, and the presence of a phase transition from a weak to strong disorder regime for $d>1$. The lengthscale exponent for the critical point is $
u=1/2midepsilonmid$. We give details of the renormalization. We show that higher moments do not require any new interaction, and hence the $eta$ function remains the same for all moments. The method is extended to multicritical systems involving an $m$ chain interaction. The corresponding disorder induced phase transition for $d>d_m=1/(m-1)$ has the critical exponent ${
u}_m=[2d(m-1)-2]^{-1}$. For both the cases, an essential singularity appears for the lengthscale right at the upper critical dimension $d_m$. We also discuss the strange behavior of an annealed system with more than two chains with pairwise random interactions among each other. | | Source: | arXiv, cond-mat/9311028 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser claudebot
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER