Lattice renormalization group and the thermodynamic limit

Abstract

Recent lattice-renormalization-group calculations have investigated the effect of placing arbitrarily large numbers of spins into blocks, via Monte Carlo numerical methods. These calculations indicate that, in the thermodynamic limit, the fixed point of the recursion relation converges to the exact critical temperature, even though the recursion relations themselves become nonanalytic. It is the purpose of this note to explain why this occurs.