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Fock Dimers Limit Shapes

This is a repository accompanying the papers 1, 2. It consists of these essential parts:

  1. Schottky uniformizations for definition of an M-curve and computation of corresponding differentials and theta functions. This uses the jtem riemann project.
  2. Creation of Z2 and Hex lattices with Fock weights corresponding to a choice of Harnack data.
  3. Simulation and visualization of dimer configurations on a weighted graph. Simulation can run on a CUDA enabled GPU or multithreaded on CPU.
  4. Calculation of limiting arctic curves and height functions based on Harnack data.

Recommended installation procedure

  1. Use VSCode as environment
  2. Install the java plugin in VSCode
  3. Install Maven. This is a dependency manager for Java that will help install necessary libraries.
  4. Run a script that you want.
    1. For dimer simulation scripts see the dimerSim folder E.g. RunSimulations
    2. For fun with theta functions see e.g. the Fay Identity verification