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

dc.contributor.authorPrellberg, Thomasen
dc.contributor.committeechairSlawny, Josephen
dc.contributor.committeememberKlaus, Martinen
dc.contributor.committeememberZia, Royce K. P.en
dc.contributor.committeememberBowden, Robert L.en
dc.contributor.committeememberHagedorn, Georgeen
dc.contributor.departmentPhysicsen
dc.date.accessioned2014-03-14T21:21:12Zen
dc.date.adate2005-10-14en
dc.date.available2014-03-14T21:21:12Zen
dc.date.issued1991en
dc.date.rdate2005-10-14en
dc.date.sdate2005-10-14en
dc.description.abstractWe 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.en
dc.description.degreePh. D.en
dc.format.extentix, 95 leavesen
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-10142005-103054en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-10142005-103054/en
dc.identifier.urihttp://hdl.handle.net/10919/39862en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartLD5655.V856_1991.P746.pdfen
dc.relation.isformatofOCLC# 24367478en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V856 1991.P746en
dc.subject.lcshPhase transformations (Statistical physics)en
dc.subject.lcshThermodynamics -- Researchen
dc.titleMaps of intervals with indifferent fixed points: thermodynamic formalism and phase transitionsen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplinePhysicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

Files

Original bundle
Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
LD5655.V856_1991.P746.pdf
Size:
2.86 MB
Format:
Adobe Portable Document Format
Description: