Phase transitions in the thermodynamic formalism of multifractals
Abstract
Nonanalyticities in the generalized dimensions of multifractal sets of physical interest are interpreted as phase transitions. The problem is mapped onto thermodynamics of one-dimensional spin models. The spin Hamiltonians are explicitly constructed and their phase transitions discussed. This mapping can provide insight in both directions.
- Publication:
-
Physical Review Letters
- Pub Date:
- March 1987
- DOI:
- Bibcode:
- 1987PhRvL..58.1169K
- Keywords:
-
- Fractals;
- Phase Transformations;
- Thermodynamics;
- Hamiltonian Functions;
- Mapping;
- Scaling;
- Set Theory;
- Thermodynamics and Statistical Physics;
- 05.70.-a;
- Thermodynamics