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Innovative computational methods for spin function extraction in Ising models via effective fields

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  • de Albuquerque, Douglas F.

Abstract

Recent advances in symbolic computation have revolutionized the evaluation of complex mathematical expressions in statistical physics. This work presents a novel methodology implemented in Maple software for efficient spin function extraction in Ising models using effective fields. Our approach optimizes algebraic operations, automates symmetry-based simplifications, and reduces computational intensity, achieving up to a 50% reduction in processing time compared to traditional methods. We demonstrate the method’s efficacy through a case study involving differential operators and symmetry properties, yielding simplified expressions for physical quantities. The technique is generalizable to multi-variable scenarios and applicable to related models, such as the Heisenberg model, offering significant practical advantages for researchers in statistical physics and beyond.

Suggested Citation

  • de Albuquerque, Douglas F., 2025. "Innovative computational methods for spin function extraction in Ising models via effective fields," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 676(C).
    • Handle: RePEc:eee:phsmap:v:676:y:2025:i:c:s0378437125005151
    DOI: 10.1016/j.physa.2025.130863
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