Abstract
This chapter focuses on logical polymers. Matrix logical fixed points are important for the understanding of cognitive phenomena. The objective is to gain new insight into the relation between logical fixed points and duality. The chapter further discusses phase transition. A two-dimensional system of Ising spins on a square lattice is known to be equivalent to a dual spin system on an inverse lattice. If the original system is at temperature T, the dual system has temperature 1/T. This symmetry allows high and low temperatures to be exchanged, with a phase transition occurring at the critical temperature, T=I. The Ising duality has nonlinear analogues in field theory where instead of a classical spacetime one has the corresponding two-dimensional field theory. By mirror symmetry, two apparently distinct spacetimes turn out to be equivalent, corresponding to equivalent two-dimensional field theories.
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