Comment on “Effect of long-range interactions on the critical behavior of the continuous Ising model” (original) (raw)

This commentary addresses the findings of a prior article regarding the critical behavior of the continuous Ising model, particularly the claims about the existence of a proper ordering transition at finite temperatures in dimensions 1 and 1.1. The authors argue that mathematical results suggest that no such transition exists for these dimensions, while it is noted that for dimension 2 and a specific anisotropic case, the ground-state energy diverges logarithmically with increasing system size, implying an infinite transition temperature. The commentary provides a more general framework for the interaction models and highlights the importance of correlation inequalities in understanding the transition behavior of these models.