A Marginal Dimension of a Weakly Diluted Quenched m-Vector Model
| dc.creator | Holovatch, Yu. | |
| dc.creator | Dudka, M. | |
| dc.creator | Yavors'kii, T. | |
| dc.date | 2002-04-05 | |
| dc.date.accessioned | 2026-07-07T02:44:57Z | |
| dc.date.available | 2026-07-07T02:44:57Z | |
| dc.description | We calculate a marginal order parameter dimension $m_c$ which in a weakly diluted quenched $m$-vector model controls the crossover from a universality class of a ``pure'' model ($m>m_c$) to a new universality class ($m<m_c$). Exploiting the Harris criterion and the field-theoretical renormalization group approach allows us to obtain $m_c$ as a five-loop $ε$-expansion as well as a six-loop pseudo-$ε$ expansion. In order to estimate the numerical value of $m_c$ we process the series by precisely adjusted Padé--Borel--Leroy resummation procedures. Our final result $m_c=1.912\pm0.004<2$ stems from the longer and more reliable pseudo-$ε$ expansion, suggesting that a weak quenched disorder does not change the values of $xy$-model critical exponents as it follows from the experiments on critical properties of ${\rm He}^4$ in porous media. | |
| dc.description | 6 pages, 4 figures, 2 style files | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0204145 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0204145 | |
| dc.identifier | J. Phys. Stud., Vol. 5, No 3/4 (2001) pp. 233-239 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/19137 | |
| dc.subject | Condensed Matter | |
| dc.title | A Marginal Dimension of a Weakly Diluted Quenched m-Vector Model | |
| dc.type | text |