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Neumann boundary conditions with null external quasi-momenta in finite systems

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Abstract.

The order parameter of a critical system defined in a layered parallel plate geometry subject to Neumann boundary conditions at the limiting surfaces is studied. We utilize a one-particle irreducible vertex parts framework in order to study the critical behavior of such a system. The renormalized vertex parts are defined at zero external quasi-momenta, which makes the analysis particularly simple. The distance between the boundary plates L characterizing the finite-size system direction perpendicular to the hyperplanes plays a similar role, here, in comparison with our recent unified treatment for Neumann and Dirichlet boundary conditions. Critical exponents are computed using diagrammatic expansion at least up to two-loop order and are shown to be identical to those from the bulk theory (limit \( L \rightarrow \infty\).

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Authors and Affiliations

  1. Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, 50670-901, Recife, PE, Brazil

    Messias V. S. Santos, José B. da Silva Jr. & Marcelo M. Leite

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  1. Messias V. S. Santos
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  2. José B. da Silva Jr.
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  3. Marcelo M. Leite
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Correspondence to Marcelo M. Leite.

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Santos, M.V.S., da Silva, J.B. & Leite, M.M. Neumann boundary conditions with null external quasi-momenta in finite systems. Eur. Phys. J. Plus 134, 372 (2019). https://doi.org/10.1140/epjp/i2019-12757-0

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