Properties of renormalization group transformations

Optimization of Renormalization Group Transformations

This thesis examines the optimization of renormaiization group transformations. To do this I have examined simple spin models where some understanding of the problems which arise and particularly the systematic errors can be acquired. In the first chapter I have given a brief description of critical phenomena which provides the motivation for the study of the renormalization group in this rest ...

Renormalization-group transformations and correlations of seismicity.

The effect of transformations analogous to those of the real-space renormalization group are analyzed for the temporal occurrence of earthquakes. A recently reported scaling law for the distribution of recurrence times implies that these distributions must be invariant under such transformations, for which the role of the correlations between the magnitudes and the recurrence times are fundamen...

Block renormalization group transformations and overlap fermions

In this preliminary work, I provide the outline of an argument (leaving the full proof to a future publication) that there exists a valid renormalization group blocking transformation which converts the continuum fermion action into a Ginsparg-Wilson lattice action. I construct the blocking for the massless overlap operator as a specific example, indicating how other Ginsparg-Wilson lattice Dir...

Variational Approximations for Renormalization Group Transformations

A p p r o x i m a t e r ecur s ion re la t ions wh ich give uppe r a n d lower b o u n d s on the free energy are descr ibed. Op t i ma l ca lcula t ions o f the free energy can t hen be ob ta ined by t rea t ing pa r ame t e r s wi th in the r eno rma l i za t ion equat ions var ia t ional ly . As an example , a par t icular ly s imple lower b o u n d a p p r o x i m a t i o n which preserves ...

Renormalization Group Renormalization Group