VISUALIZATION OF GRAPHICAL METHODS OF SERIES ANALYSIS

Abstract

Exact power series expansions provide a powerful method for studying the critical behaviour of many systems. Efficient analysis methods are essential to fully exploit the series approach. A particularly challenging problem in the analysis of these expansions is the elucidation of the critical behaviour in cases where critical temperature (or threshold) as well as dominant and correction exponent is unknown. We describe a scheme (which we call Visualization of Graphical methods for Series analysis, or VGS) developed explicitly for this situation and discuss its high precision implementation in a workstation environment. Our approach involves visualization of multiple approximants in a three-dimensional space. Several examples from Ising models, percolation and exactly solved systems are given.