On the mean-field equations for ferromagnetic spin systems (Q2230651)

In this paper the authors provide an inequality which provides upper bounds on the finite-size corrections for the magnetisation of various Ising models, in external fields, and which satisfy a mean-field equation in the thermodynamic (infinite-volume) limit. The approach reminds somewhat of Newman's analysis of Ising magnetisations in terms of the Burgers equation. The authors come to it here by noticing an analogy to a result in random matrix theory.