Bhattacharjee, S. M. ; Rao, S. Suresh (1992) Randomness in vertex models and directed walks Journal of Physics A: Mathematical and General, 25 (14). L901-L905. ISSN 0305-4470
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Official URL: http://iopscience.iop.org/0305-4470/25/14/007
Related URL: http://dx.doi.org/10.1088/0305-4470/25/14/007
Abstract
The authors consider a d-dimensional random five vertex (modified KDP) model where the vertex energies are site dependent, uncorrelated random numbers (>0). This model maps onto many directed walks in a random environment. They show that the upper critical dimension of the random vertex model is 2. They obtain a bound v>or=3/(d+3) for the size exponent of a directed walk in a random medium. The breakdown of hyperscaling in the vertex model is connected to the anomalous growth of the free energy with an exponent consistent with the corresponding one (chi =2-1/v) for a single directed walk.
| Item Type: | Article |
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| Source: | Copyright of this article belongs to Institute of Physics. |
| ID Code: | 3071 |
| Deposited On: | 09 Oct 2010 10:11 |
| Last Modified: | 19 May 2011 10:34 |
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