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The advent of quantum computing has heralded a renewed interest in physicalmemories - physically realizable structures that offer reliable data storagewith error correction only at the point of access. Here, we examine a model ofa classical physical memory, capable of storing a classical bit, based on theferromagnetic Ising model on 1- and 2-dimensional square lattices. We make useof Monte-Carlo simulations as well as analytic solutions in the hightemperature limit. At high temperatures, both 1- and 2-D Ising models behavelike a non-interacting model, albeit with a reduced effective number of spinsand a reduced effective spin-flip rate. In agreement with general arguments, weconfirm numerically that (i) the information storage time is independent ofsystem size in 1D, (ii) in two dimensions, at temperatures below the Onsagerphase transition temperature T, the information storage time increasesexponentially with system size. Interestingly, some benefit in increasingsystem size is found even above T, although the increase in lifetime is notexponential.

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