caa a22 4500 467892245 CHVBK 20180406152752.0 cr unu---uuuuu 170328e20060401xx s 000 0 eng 10.1007/s10955-006-9034-x doi (NATIONALLICENCE)springer-10.1007/s10955-006-9034-x Cluster Approximation for the Farey Fraction Spin Chain [Elektronische Daten] [Thomas Prellberg, Jan Fiala, Peter Kleban] We consider the Farey fraction spin chain in an external field h. Utilising ideas from dynamical systems, the free energy of the model is derived by means of an effective cluster energy approximation. This approximation is valid for divergent cluster sizes, and hence appropriate for the discussion of the magnetizing transition. We calculate the phase boundaries and the scaling of the free energy. At h = 0 we reproduce the rigorously known asymptotic temperature dependence of the free energy. For h ≠ 0, our results are largely consistent with those found previously using mean field theory and renormalization group arguments. Springer Science + Business Media, Inc., 2006 Phase transition nationallicence Farey fractions nationallicence spin chain nationallicence cluster approximation nationallicence Prellberg Thomas School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, E1 4NS, London, United Kingdom aut Fiala Jan Department of Physics, Clark University, 01610, Worcester, MA, USA aut Kleban Peter LASST and Department of Physics and Astronomy, University of Maine, 04469, Orono, ME, USA aut Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 123/2(2006-04-01), 455-471 0022-4715 123:2<455 2006 123 10955 https://doi.org/10.1007/s10955-006-9034-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-006-9034-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Prellberg Thomas School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, E1 4NS, London, United Kingdom aut NATIONALLICENCE 700 1- Fiala Jan Department of Physics, Clark University, 01610, Worcester, MA, USA aut NATIONALLICENCE 700 1- Kleban Peter LASST and Department of Physics and Astronomy, University of Maine, 04469, Orono, ME, USA aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 123/2(2006-04-01), 455-471 0022-4715 123:2<455 2006 123 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer