Residual entropy of the square Ising antiferromagnet in the maximum critical field: The Fibonacci matrix
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1997
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We find the analytical expression for the residual entropy of the square Ising model with nearest-neighbour antiferromagnetic coupling J, in the maximum critical field H-c = 4J, in terms of the Fibonacci matrix, which itself represents a self-similar, fractal object. The result coincides with the existing numerical data. By considering regular self-similar fractal objects rather than seemingly random transfer matrices, this approach opens the possibility of finding the corresponding solutions in more complicated cases, such as the antiferromagnets with longer than nearest-neighbour interactions and the three-dimensional antiferromagnets, as well as the possibility of unification of results pertinent to different lattices in two and three dimensions.
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Journal of Physics. A: Mathematical and General, 1997, 30, 10, L331-L337Note:
- Letter to the editor
DOI: 10.1088/0305-4470/30/10/006
ISSN: 0305-4470
WoS: A1997XC27300006
Scopus: 2-s2.0-0031582362
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VinčaTY - JOUR AU - Stošić, Borko D. AU - Stošić, Tatijana AU - Fittipaldi, Ivon P. AU - Veerman, J.J.P. PY - 1997 UR - https://vinar.vin.bg.ac.rs/handle/123456789/2071 AB - We find the analytical expression for the residual entropy of the square Ising model with nearest-neighbour antiferromagnetic coupling J, in the maximum critical field H-c = 4J, in terms of the Fibonacci matrix, which itself represents a self-similar, fractal object. The result coincides with the existing numerical data. By considering regular self-similar fractal objects rather than seemingly random transfer matrices, this approach opens the possibility of finding the corresponding solutions in more complicated cases, such as the antiferromagnets with longer than nearest-neighbour interactions and the three-dimensional antiferromagnets, as well as the possibility of unification of results pertinent to different lattices in two and three dimensions. T2 - Journal of Physics. A: Mathematical and General T1 - Residual entropy of the square Ising antiferromagnet in the maximum critical field: The Fibonacci matrix VL - 30 IS - 10 SP - L331 EP - L337 DO - 10.1088/0305-4470/30/10/006 ER -
@article{ author = "Stošić, Borko D. and Stošić, Tatijana and Fittipaldi, Ivon P. and Veerman, J.J.P.", year = "1997", abstract = "We find the analytical expression for the residual entropy of the square Ising model with nearest-neighbour antiferromagnetic coupling J, in the maximum critical field H-c = 4J, in terms of the Fibonacci matrix, which itself represents a self-similar, fractal object. The result coincides with the existing numerical data. By considering regular self-similar fractal objects rather than seemingly random transfer matrices, this approach opens the possibility of finding the corresponding solutions in more complicated cases, such as the antiferromagnets with longer than nearest-neighbour interactions and the three-dimensional antiferromagnets, as well as the possibility of unification of results pertinent to different lattices in two and three dimensions.", journal = "Journal of Physics. A: Mathematical and General", title = "Residual entropy of the square Ising antiferromagnet in the maximum critical field: The Fibonacci matrix", volume = "30", number = "10", pages = "L331-L337", doi = "10.1088/0305-4470/30/10/006" }
Stošić, B. D., Stošić, T., Fittipaldi, I. P.,& Veerman, J.J.P.. (1997). Residual entropy of the square Ising antiferromagnet in the maximum critical field: The Fibonacci matrix. in Journal of Physics. A: Mathematical and General, 30(10), L331-L337. https://doi.org/10.1088/0305-4470/30/10/006
Stošić BD, Stošić T, Fittipaldi IP, Veerman J. Residual entropy of the square Ising antiferromagnet in the maximum critical field: The Fibonacci matrix. in Journal of Physics. A: Mathematical and General. 1997;30(10):L331-L337. doi:10.1088/0305-4470/30/10/006 .
Stošić, Borko D., Stošić, Tatijana, Fittipaldi, Ivon P., Veerman, J.J.P., "Residual entropy of the square Ising antiferromagnet in the maximum critical field: The Fibonacci matrix" in Journal of Physics. A: Mathematical and General, 30, no. 10 (1997):L331-L337, https://doi.org/10.1088/0305-4470/30/10/006 . .