Abstract: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$^\dagger$ domination. Both of these notions depend on a parameter $p$ and we find the optimal values $p$ and $p^\dagger$ 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 $q,\tilde{q}\geq 1$ that is of independent interest.
From: Paul Cahen [view email]
[v1]
Thu, 11 Jun 2026 17:50:28 UTC (39 KB)
[v2]
Fri, 17 Jul 2026 12:43:14 UTC (41 KB)
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