Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
975857 | Physica A: Statistical Mechanics and its Applications | 2006 | 4 Pages |
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 Ï4-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.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Michael Kastner,