Description of Some Ground States by Puiseux Techniques

Let be a one-sided transitive subshift of finite type, where symbols are given by a finite spin set S , and admissible transitions are represented by an irreducible directed graph G ⊂ S × S . Let be a locally constant function (that corresponds with a local observable which makes finite-range intera...

Full description

Saved in:
Bibliographic Details
Published in:Journal of statistical physics 2012, Vol.146 (1), p.125-180
Main Authors: Garibaldi, Eduardo, Thieullen, Philippe
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Mathematical and Computational Physics
Methods
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
Toy industry
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Let be a one-sided transitive subshift of finite type, where symbols are given by a finite spin set S , and admissible transitions are represented by an irreducible directed graph G ⊂ S × S . Let be a locally constant function (that corresponds with a local observable which makes finite-range interactions). Given β >0, let μ βH be the Gibbs-equilibrium probability measure associated with the observable − βH . It is known, by using abstract considerations, that { μ βH } β >0 converges as β →+∞ to a H -minimizing probability measure called zero-temperature Gibbs measure. For weighted graphs with a small number of vertices, we describe here an algorithm (similar to the Puiseux algorithm) that gives the explicit form of on the set of ground-state configurations.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-011-0357-x