Nota de FísicaPublicado
Potts Model on Infinitely Ramified Sierpinski Gasket-Type Fractals and Algebraic Order at Antiferromagnetic Phases
F. S. Menezes; A. C. N. Magalhães
1991
Dados da publicação
- Autores
- F. S. Menezes; A. C. N. Magalhães
- Tipo
- Nota de Física
- Status
- Publicado
- Data de publicação
- 1991
- Descrição
- We propose families of infinitely ramified fractals, which we call the m-sheet Sierpinski gasket with side <math>b((mSG)_{b})\,\!</math>, on which the q-state Potts model can be exactly solvable through a Real Space Renormalisation Group <math>(RSRG)\,\!</math> technique and which presents phase transitions at ''finite'' temperatures for <math>m > 1\,\!</math>. We also propose, within a cell-to-cell <math>RSRG\,\!</math> sheme, a criterion for a suitable choice of cells in the study of antiferromagnetic <math>(AF)\,\!</math> classical spin models defined on (or approximated by) multi-rooted hierarchical lattices, and apply it for the <math>AF\,\!</math> Potts model on some <math>(mSG)_b\,\!</math> fractals. Concerning the Ising model on the <math>(mSG)_2\,\!</math> family, we obtained the ''exact'' para <math>(P)\,\!</math> - ferromagnetic <math>(F)\,\!</math> critical temperature as a function of <math>m\,\!</math>; we verified that, for <math> m = 1\,\!</math> and <math>2\,\!</math> , there is no <math>AF\,\!</math> order (not even at zero temperature). We calculated the exact <math> P - F\,\!</math> and possibly exact <math> P - F\,\!</math> critical frontiers and the corresponding correlation length critical exponents for <math>q = 2, 3\,\!</math> and <math>4\,\!</math>-state Potts model on the <math>(mSG)_4\,\!</math>. The <math>AF\,\!</math> <math>q = 2\,\!</math> and <math>4\,\!</math> cases have highly degenerate ground states and each one presents, above a certain critical fractal dimension <math>D^{c}_{f}\,\!</math> <math>(q,m)\,\!</math>, an unusual low-temperature phase whose attractor occurs at a non-null temperature. We proved, for <math>q = 2\,\!</math> and <math>D_f\,\!</math> <math>(2,m) \ge 5.1\,\!</math>, that the correlations have a power law decay with distance along this entire phase.
- Ano
- 1991
- Número
- CBPF-NF-058/91
- Vínculo com tese
- Não
- Vínculo com bolsa
- Não