Grassmann techniques applied to classical spin systems

Details Grassmann techniques applied to classical spin systems Grassmann techniques applied to classical spin systems

2009-05-07

arxiv.org/abs/0905.1104v2

Condensed Matter Physics 12, 3 (2009) 463-478

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

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

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