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

Douglas F. de Albuquerque

Physica A: Statistical Mechanics and its Applications, 2025, vol. 676, issue C

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.

Keywords: Maple software; Ising models; Symbolic computation; Spin functions; Effective fields; Symmetry reduction (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:676:y:2025:i:c:s0378437125005151

DOI: 10.1016/j.physa.2025.130863

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