Partition function of the Potts model on self-similar lattices as a dynamical system and multiple transitions

Details Partition function of the Potts model on self-similar lattices as a dynamical system and multiple transitions Partition function of the Potts model on self-similar lattices as a dynamical system and multiple transitions

2010-07-23

arxiv.org/abs/1007.4082v3

Physics

Condensed Matter

Statistical Mechanics

16 pages, 12 figures, 1 table; title changed, references and discussion on multiple transitions added

Scientific paper

We present an analytic study of the Potts model partition function on two different types of self-similar lattices of triangular shape with non integer Hausdorff dimension. Both types of lattices analyzed here are interesting examples of non-trivial thermodynamics in less than two dimensions. First, the Sierpinski gasket is considered. It is shown that, by introducing suitable geometric coefficients, it is possible to reduce the computation of the partition function to a dynamical system, whose variables are directly connected to (the arising of) frustration on macroscopic scales, and to determine the possible phases of the system. The same method is then used to analyse the Hanoi graph. Again, dynamical system theory provides a very elegant way to determine the phase diagram of the system. Then, exploiting the analysis of the basins of attractions of the corresponding dynamical systems, we construct various examples of self-similar lattices with more than one critical temperature. These multiple critical temperatures correspond to crossing phases with different degrees of frustration.

Affiliated with

Also associated with

No associations

Rating

Partition function of the Potts model on self-similar lattices as a dynamical system and multiple transitions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Partition function of the Potts model on self-similar lattices as a dynamical system and multiple transitions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Partition function of the Potts model on self-similar lattices as a dynamical system and multiple transitions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-138725