When topology triggers a phase transition
Abstract
Two mathematical mechanisms, responsible for the generation of a thermodynamic singularity, are individuated. For a class of short-range, confining potentials, a topology change in some family of configuration space submanifolds is the only possible such mechanism. Two examples of systems in which the phase transition is not accompanied by a such topology change are discussed. The first one is a model with long-range interactions, namely the mean-field phi^4-model, the second example is a one-dimensional system with a non-confining potential energy function. For both these systems, the thermodynamic singularity is generated by a maximization over one variable (or one discrete index) of a smooth function, although the context in which the maximization occurs is very different.
Cite
@article{arxiv.cond-mat/0509136,
title = {When topology triggers a phase transition},
author = {Michael Kastner},
journal= {arXiv preprint arXiv:cond-mat/0509136},
year = {2008}
}
Comments
Talk given at the Next-SigmaPhi conference in Kolymbari, Crete, Greece, August 13-18, 2005