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Ising model partition-function computation as a weighted counting problem.

Shaan Nagy1,2, Roger Paredes3, Jeffrey M Dudek1

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Summary
This summary is machine-generated.

This study connects the Ising model to computational problems like weighted model counting (WMC) and constraint satisfaction problems (#CSP). A new approach using TensorOrder model counter shows improved performance for Ising partition function computation.

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Area of Science:

  • Computational Physics
  • Computer Science
  • Statistical Mechanics

Background:

  • The Ising model, traditionally used in physics, offers a powerful framework for analyzing complex systems due to its combinatorial nature.
  • Understanding the computational aspects of the Ising model is crucial for its application in diverse scientific and engineering fields.

Purpose of the Study:

  • To explore the Ising model from a computational perspective, bridging it with weighted model counting (WMC) and constraint satisfaction problems (#CSP).
  • To evaluate the effectiveness of existing computational tools and develop new strategies for solving Ising-related problems.

Main Methods:

  • Reducing the Ising partition function computation problem (#Ising) to weighted model counting (WMC).
  • Applying off-the-shelf model counters, specifically TensorOrder, to solve #Ising instances.
  • Analyzing the computational complexity of #Ising by relating it to #CSP and leveraging known dichotomy results.

Main Results:

  • Demonstrated that #Ising can be effectively solved using WMC techniques.
  • Showcased that the TensorOrder model counter surpasses current state-of-the-art tools for midsize, topologically unstructured #Ising instances.
  • Provided a clear understanding of the hardness of #Ising by connecting it to #CSP complexity.

Conclusions:

  • The integration of WMC offers a novel and efficient approach to tackling #Ising.
  • TensorOrder presents a valuable tool for partition function solvers in computational physics and related fields.
  • The complexity analysis deepens our understanding of the computational challenges inherent in Ising model analysis.