Solvable lattice gas models of random hetero-polymers at finite density: I. Statics
J. van Mourik
Department of Mathematics,
King's College London, Strand, London WC2R 2LS, UK, and
Istituto Nazionale di Fisica della Materia,
Via Beirut 2-4, 34014 Trieste, Italy
jvmourik@mth.kcl.ac.uk
Received 15 June 1999 and Received in final form 14 October 1999
Abstract
We introduce 
-dimensional lattice gas versions of three
common models of random hetero-polymers, in which both the polymer density
and the density of the polymer-solvent mixture are finite. These solvable
models give valuable insight into the problems related to the (quenched)
average over the randomness in statistical mechanical models of proteins,
without having to deal with the hard geometrical constraints occurring in
finite-dimensional models.
Our exact solution, which is specific to the -dimensional case,
is compared to the results obtained by a saddle-point analysis and
by the grand ensemble approach, both of which can also be applied to
models of finite dimension. We find, somewhat surprisingly, that the
saddle-point analysis can lead to qualitatively incorrect results.
PACS
61.41.+e Polymers, elastomers, and plastics -
75.10.Nr Spin-glass and other random models
Copyright EDP Sciences, Società Italiana di Fisica, Springer-Verlag
