= Finite-ring parity qualification of an Ising quasiparticle gap
A bulk <quasiparticle> energy is not automatically the first excitation gap of a finite periodic <spin> chain. The <Jordan–Wigner transformation> fixes a boundary condition through <fermion parity> and restricts occupations to that same parity. At zero transverse field an Ising domain wall costs 2J, but periodic spin configurations contain an even number of walls; the first wall-pair excitation costs 4J. An ordered finite chain also has a distinct small symmetry-sector splitting at nonzero field. The thermodynamic dispersion and these finite-system scales answer different questions.
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