Dimensional Reduction for Directed Branched Polymers
| dc.creator | Imbrie, John Z. | |
| dc.date | 2004-02-27 | |
| dc.date | 2004-03-15 | |
| dc.date.accessioned | 2026-07-07T04:30:59Z | |
| dc.date.available | 2026-07-07T04:30:59Z | |
| dc.description | Dimensional reduction occurs when the critical behavior of one system can be related to that of another system in a lower dimension. We show that this occurs for directed branched polymers (DBP) by giving an exact relationship between DBP models in D+1 dimensions and repulsive gases at negative activity in D dimensions. This implies relations between exponents of the two models: $γ(D+1)=α(D)$ (the exponent describing the singularity of the pressure), and $ν_{\perp}(D+1)=ν(D)$ (the correlation length exponent of the repulsive gas). It also leads to the relation $θ(D+1)=1+σ(D)$, where $σ(D)$ is the Yang-Lee edge exponent. We derive exact expressions for the number of DBP of size N in two dimensions. | |
| dc.description | 7 pages, 1 eps figure, ref 24 corrected | |
| dc.identifier | https://arxiv.org/abs/math-ph/0402074 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0402074 | |
| dc.identifier | J. Phys. A: Math. Gen. 37, L137--L142 (2004) | |
| dc.identifier | doi:10.1088/0305-4470/37/12/L03 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/57664 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Statistical Mechanics | |
| dc.subject | 82B41, 82B27, 82B21, 82B20 | |
| dc.title | Dimensional Reduction for Directed Branched Polymers | |
| dc.type | text |