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Monte Carlo simulations for quantum field theories involving fermions

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Abstract

We present a new variant of a Monte Carlo procedure for euclidean quantum field theories with fermions. On a lattice every term contributing to the expansion of the fermion determinant is interpreted as a configuration of self-avoiding oriented closed loops which represent the fermionic vacuum fluctuations. These loops are related to Symanzik's polymer description of euclidean quantum field theory. The method is extended to the determination of fermionic Green's functions. We test our method on the Scalapino-Sugar model in one, two, three, and four dimensions. Good agreement with exactly known results is found.

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Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Göttingen, Bunsenstrasse 9, D-3400, Göttingen, Federal Republic of Germany

    M. Karowski

  2. State University of New York at Stony Brook, 11794, Stony Brook, NY, USA

    R. Schrader

  3. Institut für Theorie der Elementarteilchen, Freie Universität Berlin, Arnimallee 14, D-1000, Berlin 33

    H. J. Thun

Authors
  1. M. Karowski
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  2. R. Schrader
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  3. H. J. Thun
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Additional information

Communicated by G. Mack

On leave of absence from Freie Universität Berlin

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Karowski, M., Schrader, R. & Thun, H.J. Monte Carlo simulations for quantum field theories involving fermions. Commun.Math. Phys. 97, 5–29 (1985). https://doi.org/10.1007/BF01206176

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  • DOI: https://doi.org/10.1007/BF01206176

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