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Continued functions and critical exponents: tools for analytical continuation of divergent expressions in phase transition studies

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  • Venkat Abhignan

    (National Institute of Technology)

  • R. Sankaranarayanan

    (National Institute of Technology)

Abstract

Resummation methods using continued functions are implemented to converge divergent series appearing in perturbation problems related to continuous phase transitions in field theories. In some cases, better convergence properties are obtained using continued functions than diagonal Padé approximants, which are extensively used in literature. We check the reliability of critical exponent estimates derived previously in universality classes of O(n)-symmetric models (classical phase transitions) and Gross–Neveu–Yukawa models (quantum phase transitions) using new methods. Graphic Abstract

Suggested Citation

  • Venkat Abhignan & R. Sankaranarayanan, 2023. "Continued functions and critical exponents: tools for analytical continuation of divergent expressions in phase transition studies," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(3), pages 1-20, March.
    • Handle: RePEc:spr:eurphb:v:96:y:2023:i:3:d:10.1140_epjb_s10051-023-00494-2
    DOI: 10.1140/epjb/s10051-023-00494-2
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    References listed on IDEAS

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    1. Zi-Xiang Li & Yi-Fan Jiang & Shao-Kai Jian & Hong Yao, 2017. "Fermion-induced quantum critical points," Nature Communications, Nature, vol. 8(1), pages 1-6, December.
    2. Poland, Douglas, 1998. "Summation of series in statistical mechanics by continued exponentials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 250(1), pages 394-422.
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