Selfconsistent calculation of real space renormalization group flows and effective potentials
Abstract
We show how to compute real space renormalization group flows in lattice field theory by a selfconsistent method which is designed to preserve the basic stability properties of a Boltzmann factor. Particular attention is paid to controlling the errors which come from truncating the action to a manageable form. In each step, the integration over the fluctuation field (high frequency components of the field) is performed by a saddle point method. The saddle point depends on the block spin. Higher powers of derivatives of the field are neglected in the actions, but no polynomial approximation in the field is made. The flow preserves a simple parameterization of the action. In the first part the method is described and numerical results are presented. In the second part we discuss an improvement of the method where the saddle point approximation is preceded by selfconsistent normal ordering, i.e. solution of a gap equation. In the third part we describe a general procedure to obtain higher order corrections with the help of SchwingerDyson equations. In this paper we treat scalar field theories as an example. The basic limitations of the method are also discussed. They come from a possible breakdown of stability which may occur when a composite block spin or block variables for domain walls would be needed.
 Publication:

Nuclear Physics B
 Pub Date:
 February 1996
 DOI:
 10.1016/05503213(96)003409
 arXiv:
 arXiv:heplat/9602014
 Bibcode:
 1996NuPhB.477..878G
 Keywords:

 High Energy Physics  Lattice;
 High Energy Physics  Theory
 EPrint:
 52 pages, uses pstricks macro, three psfigures