Abstract
The author derives certain properties of Sompolinsky's mean field theory (1981) of spin glasses showing its consistency. He obtains an exact relation which replaces the Parisi-Toulouse hypothesis (1980). Parisi's parameter X is identified with an averaged squared 3-spin vertex. He expands the solution along the de Almeida-Thouless line (1978) using a Parisi-type differential equation for the free energy.
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