Physics NotePublished
One-dimensional Potts model with iong-range interactions: a renormalization group approach
S. A. Cannas; A. C. N. Magalhães
1995
Publication details
- Authors
- S. A. Cannas; A. C. N. Magalhães
- Type
- Physics Note
- Status
- Published
- Publication date
- 1995
- Description
- The one-dimensional q-state Potts model with ferromagnetic pair interactions which decay with the distance r as <math>1/r^{\alpha}\,\!</math> is considered. We calculate, through a real-space renormalization group technique using Kadanoff blocks of length b, the critical temperature <math>T_c (b,q,\alpha )\!\,</math> and the correlation-length critical exponent <math>\nu (b,q,\alpha ) \!\,</math> as a function of <math>\alpha \!\,</math> for different values of <math>q\!\,</math>. Some of the very few known rigorous results for general <math>q\!\,</math> are reproduced by our approach. Several asymptotic behaviours are derived analytically for <math>q = 2\!\,</math> and <math>3\!\,</math> in the <math>b\rightarrow \infty\!\,</math> limit. We also obtain extrapolated critical temperatures <math>(b = \infty )\!\, </math> for arbitrary values of <math>\alpha > 1\!\,</math> and for <math>q = 2,3\!\,</math> and <math>4\!\,</math>, which we believe approximate well the exact ones. In particular, we conjecture that the exact critical temperature <math>T_c (q, \alpha =2)\!\,</math> is the same for any value of <math>q\!\,</math>. Furthermore, we verified that <math>T_c (q, \alpha \rightarrow 1) \propto (\alpha - 1)^{-1}\forall q\!\, </math>, which is consistent with a recent conjecture of Tsallis.
- Year
- 1995
- Number
- CBPF-NF-090/95
- Linked to a thesis
- No
- Linked to a grant
- No