In the eigen microstate approach(EMA),phase emergence is signaled by the condensation of an eigen microstate with a finite eigenvalue.The associated eigenvalue acts as an order parameter,exhibiting finite-size scaling...In the eigen microstate approach(EMA),phase emergence is signaled by the condensation of an eigen microstate with a finite eigenvalue.The associated eigenvalue acts as an order parameter,exhibiting finite-size scaling(FSS)behaviors within the critical regime.The eigen microstate derived from EMA precisely characterizes the spatial structure of the emergent phase,which remains less explored in systems lacking translational invariance.Here,we propose an FSS form for the eigen microstate itself and numerically validate it using the two-dimensional Ising model under various boundary conditions.This result enables the derivation of FSS relations for correlation functions,which we verify through numerical simulations.Our results complete the FSS formalism for the EMA.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12405032,12135003,and 11947231)。
文摘In the eigen microstate approach(EMA),phase emergence is signaled by the condensation of an eigen microstate with a finite eigenvalue.The associated eigenvalue acts as an order parameter,exhibiting finite-size scaling(FSS)behaviors within the critical regime.The eigen microstate derived from EMA precisely characterizes the spatial structure of the emergent phase,which remains less explored in systems lacking translational invariance.Here,we propose an FSS form for the eigen microstate itself and numerically validate it using the two-dimensional Ising model under various boundary conditions.This result enables the derivation of FSS relations for correlation functions,which we verify through numerical simulations.Our results complete the FSS formalism for the EMA.
