2026/06/11 by Paul Cahen, Avelio Sepúlveda
#math.PR
At first glance, one would imagine that the energy field of the Ising model, the set of edges whose endpoints share the same spin, is stochastically monotone as a function of the coupling constants. However, this is not generally the case. In this paper, we introduce two weaker notions of stochastic domination that make this result true: p--weak and p--weak^† domination. Both of these notions depend on a parameter p and we find the optimal values p and p^† so that these dominations hold. One of the key ingredient to obtain some of the results is a new stochastic domination relating FK percolations with different parameters q,q≥ 1 that is of independent interest.