Nota de FísicaPublicado
Criticality of the Discrete N-Vector Ferromagnet in Planar Self-Dual Lattices
C. Tsallis; A. M. Mariz; A. Stella; L. R. Silva
1989
Datos de la publicación
- Autores
- C. Tsallis; A. M. Mariz; A. Stella; L. R. Silva
- Tipo
- Nota de Física
- Estado
- Publicado
- Fecha de publicación
- 1989
- Descripción
- We study an extended version of the discrete N-vector (or cubic) ferromagnetic model within a real space renormalization group approach which preserves the two-spin correlation function. The N−evolution (for ''real'' values of N) of the Wheatstone-bridge hierarchical lattice phase diagram, which presents paramagnetic, intermediate (nematic-like) and ferromagnetic phases, as well as of the thermal (<math>\nu </math>) and crossover (<math>\varnothing </math>) critical exponents, is presented. The self-avoiding walk problem is recovered in the N <math> \to </math> 0 limit, and the so called "corner-rule" is reobtained in a larger context. The Ising, N- and 2N-state Potts ferromagnets are recovered as particular cases. An interchange of stability occurs at N = N* <math>\simeq </math> 6.9 in such a way that the 2N-state Potts special point (where all three existing phases join) is a multicritical one if N < N* but only a critical one if N > N* (consistently <math>\varnothing </math>(N*)=0). For the cubic model, <math>\nu </math>(N) presents a maximum at N = N<sub>max</sub> <math>\simeq </math>1.5. The results are exact, for all N, for the Wheatstone-bridge hierarchical lattice, and approximate, for N <math> \leqslant </math> 2, for the square lattice. Last but not least, we discuss the connection between the present approach and the phenomenological renormalization group.
- Año
- 1989
- Número
- CBPF-NF-017/89
- Vínculo con tesis
- No
- Vínculo con beca
- No