Grassmann techniques applied to classical spin systems

Grassmann techniques applied to classical spin systems

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 cr...

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Main Authors: M. Clusel, J.-Y. Fortin
Format: Article
Language:English
Published: Institute for Condensed Matter Physics 2009-01-01
Series:Condensed Matter Physics
Subjects:
Grassmann algebra
spin systems
critical phenomena
Online Access:http://dx.doi.org/10.5488/CMP.12.3.463
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spelling doaj-661fa91c32f0400da4510c878853f79f2020-11-24T23:36:38ZengInstitute for Condensed Matter PhysicsCondensed Matter Physics1607-324X2009-01-01123463478Grassmann techniques applied to classical spin systemsM. CluselJ.-Y. FortinWe 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.http://dx.doi.org/10.5488/CMP.12.3.463Grassmann algebraspin systemscritical phenomena
collection DOAJ
language English
format Article
sources DOAJ
author M. Clusel
J.-Y. Fortin
spellingShingle M. Clusel
J.-Y. Fortin
Grassmann techniques applied to classical spin systems
Condensed Matter Physics
Grassmann algebra
spin systems
critical phenomena
author_facet M. Clusel
J.-Y. Fortin
author_sort M. Clusel
title Grassmann techniques applied to classical spin systems
title_short Grassmann techniques applied to classical spin systems
title_full Grassmann techniques applied to classical spin systems
title_fullStr Grassmann techniques applied to classical spin systems
title_full_unstemmed Grassmann techniques applied to classical spin systems
title_sort grassmann techniques applied to classical spin systems
publisher Institute for Condensed Matter Physics
series Condensed Matter Physics
issn 1607-324X
publishDate 2009-01-01
description 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.
topic Grassmann algebra
spin systems
critical phenomena
url http://dx.doi.org/10.5488/CMP.12.3.463
work_keys_str_mv AT mclusel grassmanntechniquesappliedtoclassicalspinsystems
AT jyfortin grassmanntechniquesappliedtoclassicalspinsystems
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