Thermal Operators in Ising Percolation
Abstract
We discuss a new cluster representation for the internal energy and the specific heat of the d-dimensional (d=2,3,4) Ising model, obtained by studying the percolation mapping of an Ising model with frustrated links. Such a representation relates the thermal operators to the topological properties of the Fortuin-Kasteleyn clusters of Ising percolation and is a powerful tool to get new exact relations on the topological structure of FK clusters in any space dimension. As an application we show that the thermal critical index of the Ising model is related to the fractal dimension of a special topological subset of bonds (the set of ``cutting pairs''), thus answering to a long-standing open question in Ising percolation.Keywords
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