Title: Renormalization group maps for Ising models in lattice gas variables
We consider real space renormalization group maps, e.g., the
majority rule transformation, in the lattice gas variables.
We show that in these variables individual coefficients in the
renormalized Hamiltonian only depend on a finite number of
values of the renormalized Hamiltonian. We introduce a numerical
method which computes the values of the renormalized Hamiltonian
with high accuracy and so computes the coefficients in the
lattice gas variables with high accuracy. For the criticial
nearest neighbor Ising model on the square lattice with the
majority rule transformation, we compute over 1,000 different
coefficients in the lattice gas variable representation
of the renormalized Hamiltonian and study the decay of these
coefficients. We find that they decay exponentially in some
sense but with a slow decay rate. We also show that the
coefficients in the spin variables are sensitive to the truncation
method used to compute them.
Paper archived at
http://arxiv.org/abs/0905.2601