2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/55642The XYZ spin chain with boundaries is studied. We construct the vacuum state by the vertex operators in the level one modules of the elliptic algebra, and compact it through a geometric symmetry of the model called the turning symmetry. From this simplified expression the ``finite size formula'' for magnetizations in the bounded and in the half-infinite chains is deduced. Applying this formula we calculate the spontaneous magnetization in the bounded XYZ model.14pages, LaTeX2e file, uses psfragHigh Energy Physics - TheoryCondensed MatterQuantum AlgebraExactly Solvable and Integrable Systemstext