A Statistical Model of Current Loops and Magnetic Monopoles

@article{Ayyer2013ASM,
  title={A Statistical Model of Current Loops and Magnetic Monopoles},
  author={Arvind Ayyer},
  journal={Mathematical Physics, Analysis and Geometry},
  year={2013},
  volume={18},
  pages={1-19}
}
  • A. Ayyer
  • Published 23 November 2013
  • Mathematics
  • Mathematical Physics, Analysis and Geometry
We formulate a natural model of loops and isolated vertices for arbitrary planar graphs, which we call the monopole-dimer model. We show that the partition function of this model can be expressed as a determinant. We then extend the method of Kasteleyn and Temperley-Fisher to calculate the partition function exactly in the case of rectangular grids. This partition function turns out to be a square of a polynomial with positive integer coefficients when the grid lengths are even. Finally, we… 
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9 Citations
Background Citations
3
Methods Citations
1

9 Citations

The monopole-dimer model on Cartesian products of plane graphs

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Squareness for the Monopole-Dimer Model

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    Annals of Combinatorics
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The monopole-dimer model introduced recently is an exactly solvable signed generalisation of the dimer model. We show that the partition function of the monopole-dimer model on a graph invariant…

Exact solution of the 2d dimer model: Corner free energy, correlation functions and combinatorics

A Pfaffian Formula for Monomer–Dimer Partition Functions

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A Pfaffian Formula for Monomer–Dimer Partition Functions

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Pfaffian Correlation Functions of Planar Dimer Covers

The Pfaffian structure of the boundary monomer correlation functions in the dimer-covering planar graph models is rederived through a combinatorial/topological argument. These functions are then…

Enumeration of Tilings

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Pfaffian Correlation Functions of Planar Dimer Covers

The Pfaffian structure of the boundary monomer correlation functions in the dimer-covering planar graph models is rederived through a combinatorial/topological argument. These functions are then…

Squareness for the Monopole-Dimer Model

The monopole-dimer model introduced recently is an exactly solvable signed generalisation of the dimer model. We show that the partition function of the monopole-dimer model on a graph invariant…

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