We study ferromagnetic Ising models on finite graphs with an inhomogeneous external field, where a subset of vertices is designated as the boundary. show that influence boundary conditions any given spin maximised when field identically 0. One corollary spin–spin correlations are vanishes and condition free, which proves conjecture Shlosman. In particular, random model $${\mathbb {Z}}^d$$ , $$d...

In this paper, a new construction method of quaternary sequences of even period 2N having the ideal autocorrelation and balance properties is proposed. These quaternary sequences are constructed by applying the inverse Gray mapping to binary sequences of odd period N with the ideal autocorrelation. Autocorrelation distribution of the proposed quaternary sequences is derived. These sequences can...