Bare coupling constant theory

The effective field-theoretical Hamiltonian of the model (14), obtained via special Stratonovich-Hubbard transformation, passing from the discrete S3 tem to the continuous field theory, is the same as (13). The relevant global properties of a microscopic model is represented by the structure of the effective Hamiltonian. In this case, is a squared bare mass proportional to the temperature distance to the critical point, o > 0 is a bare coupling constant. Note that the effective Hamiltonian (13) preserves the 0(m) symmetry of the Stanley model (14). As far as the Stanley model is in this sense equivalent to the 0(m) symmetric theory, the analytic continuation m —> 0 of this model again leads to the polymer limit. 

The calculation of the correlation functions in the field theory is well documented in the literature. For d = 4, the calculation of the various quantities encounter divergence problems (due to the presence of the cut-off A of equation (42) which are removed by the proper renormalizations of the bare mass Eq and the bare coupling constant w. The analogs of the renormalization group equations (such as those of Gellman and Low, tHooft and Veltman, and Callan and Symanzik) which describe the dependence of the correlation functions (and the vertex functions) on arbitrary scale factors can be readily written for the polymer case also. " " A study of the Wilson function, j8( ), which describes the dependence of the renormalized coupling constant g on an... 

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