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Note that the existence of finite local fields is true for states of arbitrary energy. In particular, considering the zero energy states, selected by a reweighting (Formula presented) one sees from Eq. (57) that their nontrivial cavity fields scale as (Formula presented) however when computing the local fields as in Eq. (70), the extra reweighting exactly compensates this scaling, giving finite local fields also when (Formula presented)
-
Note that the existence of finite local fields is true for states of arbitrary energy. In particular, considering the zero energy states, selected by a reweighting (Formula presented) one sees from Eq. (57) that their nontrivial cavity fields scale as (Formula presented) however when computing the local fields as in Eq. (70), the extra reweighting exactly compensates this scaling, giving finite local fields also when (Formula presented)
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