Spin- {1}/{2} lattice system. Partial-trace method and symmetry breakdown

The partition function and the correlation functions of a general spin- {1}/{2} system defined on a lattice Λ are related to the corresponding functions of a system defined on a sublattice Λ/Λ ₀. It is shown that the interactions on Λ/Λ ₀ are obtained directly from the group properties of the system and this method extends the general construction of the duality relation previously discussed. Equations for the correlation functions are derived and discussed in relation to the group structure phase transition and symmetry breakdown. Improved upper bounds for the critical temperature are obtained.