Condensed Matter Physics, 2009, vol. 12, No. 3, pp. 463-478
Grassmann techniques applied to classical spin systems
(Department of Physics and Center for Soft Matter Research, New-York University, 4 Washington place, New-York NY 10003, USA)
(Institut Jean Lamour Département de Physique de la Mati\`ere et des Matériaux, Groupe de Physique Statistique CNRS - Nancy-Université BP 70239 F-54506 Vandoeuvre les Nancy Cedex, France)
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 be 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.
Grassmann algebra, spin systems, critical phenomena
02.30.Ik, 05.50.+q, 05.70.Fh
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