https://doi.org/10.1140/epjb/e2003-00230-4
Break of universality for an Ising model with aperiodic Rudin-Shapiro interactions
Instituto de Física,
Universidade Federal da Bahia,
Campus da Federação,
40210-340 Salvador, Brazil
Corresponding author: a randrade@ufba.br
Received:
18
December
2002
Revised:
27
February
2003
Published online:
11
August
2003
We analyze the ferromagnetic Ising model on non-Euclidean scale invariant
lattices with aperiodic interactions 
defined by
Rudin-Shapiro substitution rules with Migdal-Kadanoff renormalization (MKR)
and transfer matrix (TM) techniques. The analysis of the invariant sets of
the zero-field MKR transformation indicates that the critical behavior,
completely distinct from the one of the uniform model, is described by a new
off-diagonal fixed point. This contrasts with other aperiodic models where
the new critical behavior is described by a period-two cycle. With the new
fixed point, values for the thermal critical exponents, 
and ν, as well as the period of log-periodic oscillations, are obtained. Exact
recursive maps for all thermodynamical functions are derived within the TM
approach. The explicit dependence of the thermodynamical functions with
respect to temperature is evaluated by the numerical iteration of the set of
maps until a previously chosen convergence is achieved. They also indicate
that, depending on the actual choice for the aperiodic coupling constants,
the magnetic exponents (
and γ) assume different values.
However the Rushbrook relation is always satisfied.
PACS: 05.50.+q – Lattice theory and statistics / 05.10.Cc – Renormalization group methods / 64.60.Ak – Renormalization-group, fractal, and percolation studies of phase transitions / 61.44.Br – Quasicrystals
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2003
