ORTHOGONALITY BETWEEN SCALES AND WAVELETS IN A REPRESENTATION FOR CORRELATION-FUNCTIONS - THE LATTICE DIPOLE GAS AND ((V)OVER-BAR-PHI)(4) MODELS

Exact formulas for the correlation functions of lattice scalar field m odels in Z(d), d greater than or equal to 3, such as the dipole gas an d anharmonic crystal are derived in terms of the effective action gene rated after n applications of the block renormalization group transfor mation. Utilizing the orthogonality between different momentum scales (relations due to the wavelets implicit in the structure of the block renormalization group transformation), the formulas are quite simple, isolate the dominant term, and, in the thermodynamic and n --> infinit y limits, reduce the analysis to local estimates of the effective acti on. Based on a large-small field analysis, the two-point function is d etermined and it is shown how to extend the results to general correla tions. The results proved here show the usefulness of the ''orthogonal ity-of-scales'' property for the study of correlation functions.