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Singularities of Bethe Ansatz via Robinson Numbers

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Koper A., Krasoń P., Milewski J.
Acta Physica Polonica A
|
2018
|
vol. 133
|
issue 3
438-440
EN
In this work we suggest a rigorous mathematical approach for explanation of singular solutions of Bethe Ansatz by means of Robinson complex hypernumbers. There are several approaches towards these singular solutions eg. formal infinitesimals or germs of meromorphic functions. Our aim is to make them precise using non-standard analysis and show that they are essentially equivalent.
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Critical Exponents for Metal-Insulator Transition in Two-Dimensional Systems

100%
Wojtkiewicz J.
Acta Physica Polonica A
|
2009
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vol. 115
|
issue 5
931-934
EN
Three years ago, a new universality class, associated with the metal-insulator transition in quasi-two-dimensional compounds, was discovered. Imada has given explanation of the observed critical behaviour. Considerations in this work are based on the assumption that the one-particle dispersion is quartic one instead of the standard quadratic behaviour. In this paper, it is shown that other possible natural non-standard dispersions lead to other possible critical behaviour and critical exponents.
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