Grassmann techniques applied to classical spin systems

TL;DR

This paper reviews how Grassmann techniques can be used to analyze classical 2D spin systems, linking them to fermionic field theories and aiding in critical point estimation.

Contribution

It provides a comprehensive review of Grassmann methods applied to classical spin models, highlighting their role in understanding critical behavior and estimating phase transition points.

Findings

Grassmann techniques establish exact correspondences between spin Hamiltonians and fermionic actions.

Identification of bare masses enables accurate critical point estimation.

Monte-Carlo and diagrammatic methods support the theoretical results.

Abstract

We review problems involving the use of Grassmann techniques in the field of classical spin systems in two dimensions. These techniques are useful to perform exact correspondences between classical spin Hamiltonians and field-theory fermionic actions. This contributes to a better understanding of critical behavior of these models in term of non-quadratic effective actions which can been seen as an extension of the free fermion Ising model. Within this method, identification of bare masses allows for an accurate estimation of critical points or lines and which is supported by Monte-Carlo results and diagrammatic techniques.