Ergodicity of the hard-core model on \(\mathbb{Z}^ 2\) with parity-dependent activities
Consider the hard-core model on \(\mathbb{Z}^2\) with activities \(a_e\) on the even lattice and \(a_o\) on the odd lattice. It is an old result due to Dobrushin that in the symmetric case \(a_e=a_o=a\) with \(a\) sufficiently large, the system exhibits a phase transition. We show that this does not happen when \(a_e\neq a_o\), thereby confirming the two-dimensional case of a conjecture by van den Berg and Steif.
scientific article; zbMATH DE number 1031492