Asymptotic analysis of determinant of discrete Laplacian

In this paper, we study the relation between the partition function of free scalar field theory on hypercubes with boundary conditions and asymptotics of discrete partition functions on a sequence of lattices which approximate the hypercube as the mesh approaches to zero. More precisely, we show tha...

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Bibliographic Details
Published in:Letters in mathematical physics 2020-02, Vol.110 (2), p.259-296
Main Authors: Hou, Yuhang, Kandel, Santosh
Format: Article
Language:English
Subjects:
Asymptotic series
Boundary conditions
Complex Systems
Dirichlet problem
Field theory
Geometry
Group Theory and Generalizations
Hypercubes
Lattices
Mathematical and Computational Physics
Partitions (mathematics)
Physics
Physics and Astronomy
Scalars
Theoretical
Toruses
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Summary:In this paper, we study the relation between the partition function of free scalar field theory on hypercubes with boundary conditions and asymptotics of discrete partition functions on a sequence of lattices which approximate the hypercube as the mesh approaches to zero. More precisely, we show that the logarithm of the zeta-regularized determinant of Laplacian on the hypercube with Dirichlet boundary condition appears as the constant term in the asymptotic expansion of the log determinant of the discrete Laplacian up to an explicitly computable constant. We also investigate similar problems for the massive Laplacian on tori.
ISSN:0377-9017
1573-0530
DOI:10.1007/s11005-019-01208-5