Version 1
: Received: 2 November 2024 / Approved: 4 November 2024 / Online: 5 November 2024 (08:43:36 CET)
How to cite:
Tonchev, N.; Dantchev, D. Chebyshev Polynomials in the Physics of the One-Dimensional Finite-Size Ising Model: An Alternative View and Some New Results. Preprints2024, 2024110276. https://doi.org/10.20944/preprints202411.0276.v1
Tonchev, N.; Dantchev, D. Chebyshev Polynomials in the Physics of the One-Dimensional Finite-Size Ising Model: An Alternative View and Some New Results. Preprints 2024, 2024110276. https://doi.org/10.20944/preprints202411.0276.v1
Tonchev, N.; Dantchev, D. Chebyshev Polynomials in the Physics of the One-Dimensional Finite-Size Ising Model: An Alternative View and Some New Results. Preprints2024, 2024110276. https://doi.org/10.20944/preprints202411.0276.v1
APA Style
Tonchev, N., & Dantchev, D. (2024). Chebyshev Polynomials in the Physics of the One-Dimensional Finite-Size Ising Model: An Alternative View and Some New Results. Preprints. https://doi.org/10.20944/preprints202411.0276.v1
Chicago/Turabian Style
Tonchev, N. and Daniel Dantchev. 2024 "Chebyshev Polynomials in the Physics of the One-Dimensional Finite-Size Ising Model: An Alternative View and Some New Results" Preprints. https://doi.org/10.20944/preprints202411.0276.v1
Abstract
For studying of the finite-size behavior of the Ising model under different boundary conditions we propose an alternative to the standard transfer matrix technique approach based on Abel\`{e}s theorem and Chebyshev polynomials. Using it we easily reproduce the known for periodic boundary conditions results for Lee-Yang zeros, the exact position space renormalization group transformation, etc., and extend them deriving new results for antiperiodic boundary conditions. Note that in the latter case one has a nontrivial order-parameter profile, which we also calculate, where the average value of a given spin depends on the distance from the seam with opposite bond in the system. It is interesting to stress that under both boundary conditions, the one-dimensional case exhibits Schottky anomaly.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
