摘要
We study replica symmetry breaking (RSB) for multi-entropy in the random-tensor-network (RTN) domain-wall spin model. Our main result is that, within this framework, multi-entropy has a structural obstruction to RSB for any Rényi indexnand any multipartite number𝚚 . This obstruction arises because the boundary permutations relevant to multi-entropy are organized along mutually incompatible coordinate directions of the replica hypercube, and therefore do not admit a nontrivial common geodesic intermediate permutationτin the Cayley graph ofS_(N) . This is in sharp contrast to entanglement negativity, which does admit such aτ -mediated saddle and exhibits RSB in the same framework. As a robustness check, we also consider a toyℤ₂gauge extension of the spin model with a minimal bulk gauge constraint. Numerical evidence in this gauged model indicates that multi-entropy continues to show no sign of RSB atn=2andn=3 , while negativity continues to exhibit RSB. Our results show that, within the RTN spin-model description, multi-entropy is not "RSB-friendly'': its boundary data are structurally incompatible with a nontrivial common geodesic intermediate permutation, unlike negativity.