Finite-size scaling behavior in trapped systems
| Autor: | de Queiroz, S. L. A., Santos, R. R. dos, Stinchcombe, R. B. |
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| Rok vydání: | 2010 |
| Předmět: | |
| Zdroj: | Physical Review E 81, 051122 (2010) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevE.81.051122 |
| Popis: | Numerical transfer-matrix methods are applied to two-dimensional Ising spin systems, in presence of a confining magnetic field which varies with distance $|{\vec x}|$ to a "trap center", proportionally to $(|{\vec x}|/\ell)^p$, $p>0$. On a strip geometry, the competition between the "trap size" $\ell$ and the strip width, $L$, is analysed in the context of a generalized finite-size scaling {\em ansatz}. In the low-field regime $\ell \gg L$, we use conformal-invariance concepts in conjunction with a linear-response approach to derive the appropriate ($p$-dependent) limit of the theory, which agrees very well with numerical results for magnetization profiles. For high fields $\ell \lesssim L$, correlation-length scaling data broadly confirms an existing picture of $p$-dependent characteristic exponents. Standard spin-1/2 and spin-1 Ising systems are considered, as well as the Blume-Capel model. Comment: RevTeX, 8 pages, 7 .eps figures (published version |
| Databáze: | arXiv |
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