  The advent of quantum computing has heralded a renewed interest in physical
memories - physically realizable structures that offer reliable data storage
with error correction only at the point of access. Here, we examine a model of
a classical physical memory, capable of storing a classical bit, based on the
ferromagnetic Ising model on 1- and 2-dimensional square lattices. We make use
of Monte-Carlo simulations as well as analytic solutions in the high
temperature limit. At high temperatures, both 1- and 2-D Ising models behave
like a non-interacting model, albeit with a reduced effective number of spins
and a reduced effective spin-flip rate. In agreement with general arguments, we
confirm numerically that (i) the information storage time is independent of
system size in 1D, (ii) in two dimensions, at temperatures below the Onsager
phase transition temperature T, the information storage time increases
exponentially with system size. Interestingly, some benefit in increasing
system size is found even above T, although the increase in lifetime is not
exponential.
