6 research outputs found
Asymptotics of the Farey Fraction Spin Chain Free Energy at the Critical Point
We consider the Farey fraction spin chain in an external field . Using
ideas from dynamical systems and functional analysis, we show that the free
energy in the vicinity of the second-order phase transition is given,
exactly, by
Here is a reduced
temperature, so that the deviation from the critical point is scaled by the
Lyapunov exponent of the Gauss map, . It follows that
determines the amplitude of both the specific heat and susceptibility
singularities. To our knowledge, there is only one other microscopically
defined interacting model for which the free energy near a phase transition is
known as a function of two variables.
Our results confirm what was found previously with a cluster approximation,
and show that a clustering mechanism is in fact responsible for the transition.
However, the results disagree in part with a renormalisation group treatment
Spectral analysis of dynamical systems
Available from British Library Document Supply Centre-DSC:D217950 / BLDSC - British Library Document Supply CentreSIGLEGBUnited Kingdo
Rigged Hilbert spaces for chaotic dynamical systems
We consider the problem of rigging for the Koopman operators of the Renyi and the baker maps. We show that the rigged Hilbert space for the Renyi maps has some of the properties of a strict inductive limit and give a detailed description of the rigged Hilbert space for the baker maps. © 1996 American Institute of Physics.SCOPUS: ar.jinfo:eu-repo/semantics/publishe