The Library
Telescopic linkages and a topological approach to phase transitions
Tools
Farber, Michael and Fromm, Viktor (2011) Telescopic linkages and a topological approach to phase transitions. Journal of the Australian Mathematical Society, Vol.90 (No.2). pp. 183-195. doi:10.1017/S144678871100125X ISSN 1446-7887.
Research output not available from this repository.
Request-a-Copy directly from author or use local Library Get it For Me service.
Official URL: http://dx.doi.org/10.1017/S144678871100125X
Abstract
A topological approach to the theory of equilibrium phase transitions in statistical physics is based on the topological hypothesis, which claims that phase transitions are due to changes of the topology of suitable submanifolds in the configuration space. In this paper we examine in detail the antiferromagnetic mean-field XY model and study the topology of the subenergy manifolds. The latter can be interpreted mechanically as the configuration space of a linkage with one telescopic leg. We use methods of Morse theory to describe explicitly the Betti numbers of this configuration space. We apply these results to the antiferromagnetic mean-field XY model and compute the exponential growth rate of the total Betti number. Previous authors studied the Euler characteristic rather than the total Betti number. We show that in the presence of an external magnetic field the model undergoes a single ‘total Betti number phase transition’.
Item Type: | Journal Article | ||||
---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Journal of the Australian Mathematical Society | ||||
Publisher: | Cambridge University Press | ||||
ISSN: | 1446-7887 | ||||
Official Date: | April 2011 | ||||
Dates: |
|
||||
Volume: | Vol.90 | ||||
Number: | No.2 | ||||
Page Range: | pp. 183-195 | ||||
DOI: | 10.1017/S144678871100125X | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |