Maps of intervals with indifferent fixed points: thermodynamic formalism and phase transitions

We develop the thermodynamic formalism for a large class of maps of the interval with indifferent fixed points. For such systems the formalism yields one-dimensional systems with many-body infinite range interactions for which the thermodynamics is well defined while the Gibbs states are not. (Piecewise linear systems of this kind yield the soluble, in a sense, Fisher models.) We prove that such systems exhibit phase transitions, the order of which depends on the behavior at the indifferent fixed points. We obtain the critical exponent describing the singularity of the pressure and analyse the decay of correlations of the equilibrium states at all temperatures. Our technique relies on establishing and exploiting a relationship between the transfer operators of the original map and its suitable (expanding) induced version. The technique allows one to also obtain a version of the Bowen-Ruelle formula for the Hausdorff dimension of repellers for maps with indifferent fixed points, and to generalize Fisher results to some non-soluble models.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Physics

Department dc:contributor.department

Physics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

1991

Author dc:creator

• Prellberg, Thomas

Chair dc:contributor.committeechair

• Slawny, Joseph

Committee members dc:contributor.committeemember

• Klaus, Martin
• Zia, Royce K. P.
• Bowden, Robert L.
• Hagedorn, George

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Dc Identifier Other

etd-10142005-103054

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/39862