Partition and generating function zeros in adsorbing self-avoiding walks
Abstract
The Lee-Yang theory of adsorbing self-avoiding walks is presented. It is shown that Lee-Yang zeros of the generating function of this model asymptotically accumulate uniformly on a circle in the complex plane, and that Fisher zeros of the partition function distribute in the complex plane such that a positive fraction are located in annular regions centred at the origin. These results are examined in a numerical study of adsorbing self-avoiding walks in the square and cubic lattices. The numerical data are consistent with the rigorous results; for example, Lee-Yang zeros are found to accumulate on a circle in the complex plane and a positive fraction of partition function zeros appear to accumulate on a critical circle. The radial and angular distributions of partition function zeros are also examined and it is found to be consistent with the rigorous results.
- Publication:
-
Journal of Statistical Mechanics: Theory and Experiment
- Pub Date:
- March 2017
- DOI:
- 10.1088/1742-5468/aa5ec9
- arXiv:
- arXiv:1608.01273
- Bibcode:
- 2017JSMTE..03.3208J
- Keywords:
-
- Condensed Matter - Statistical Mechanics;
- 82B41;
- 82B23
- E-Print:
- Version 3: Updated