The Ising ferromagnet as a self-correcting physical memory: a Monte-Carlo study

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.