Abstract

Fields can be represented in a discrete manner from their values at some locations, the nodes when considering finite element descriptions. Thus, each discrete scalar solution can be considered as a point in ${ℝ}^N$ ($N$ being the number of nodes used for approximating the scalar field). Most manifold learning techniques (linear and nonlinear) are based on the fact that those solutions define a slow manifold of dimension $n\ll N$ embedded in the space ${ℝ}^N$. This paper explores such a behavior in systems exhibiting phase transitions in order to analyze the evolution of the local dimensionality $n$ when the system moves from one side of the critical behavior to the other. For that purpose we consider the Ising model.

Keywords

Physics and Astronomy Classification Scheme 2010

Milestones

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