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TMF, 2017, Volume 190, Number 2, Pages 344–353 (Mi tmf9112)  

This article is cited in 1 scientific paper (total in 1 paper)

Field theory and anisotropy of a cubic ferromagnet near the Curie point

A. Kudlisab, A. I. Sokolova

a Saint Petersburg State University, St. Petersburg, Staryi Petergof, Russia
b St. Petersburg State University of Information Technologies, Mechanics and Optics, St. Petersburg, Russia

Abstract: It is known that critical fluctuations can change the effective anisotropy of a cubic ferromagnet near the Curie point. If the crystal undergoes a phase transition into the orthorhombic phase and the initial anisotropy is not too strong, then the effective anisotropy acquires the universal value $A^*=v^*/u^*$ at $T_{\mathrm c}$, where $u^*$ and $v^*$ are the coordinates of the cubic fixed point of the renormalization group equations in the scaling equation of state and expressions for nonlinear susceptibilities. Using the pseudo-$\epsilon$-expansion method, we find the numerical value of the anisotropy parameter $A$ at the critical point. Padé resummation of the six-loop pseudo-$\epsilon$-expansions for $u^*$, $v^*$, and $A^*$ leads to the estimate $A^*=0.13\pm0.01$, giving evidence that observation of anisotropic critical behavior of cubic ferromagnets in physical and computer experiments is entirely possible.

Keywords: cubic model, effective anisotropy, renormalization group, $\epsilon$-expansion, pseudo-$\epsilon$-expansion

Funding Agency Grant Number
Russian Science Foundation 16-11-10218
Russian Foundation for Basic Research 15-02-04687
The research of A. Kudlis was supported by a grant from the Russian Science Foundation (Project No. 16-11-10218).
The research of A. I. Sokolov was supported by the Russian Foundation for Basic Research (Grant No. 15-02-04687).


DOI: https://doi.org/10.4213/tmf9112

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English version:
Theoretical and Mathematical Physics, 2017, 190:2, 295–302

Bibliographic databases:

Document Type: Article
Received: 09.12.2015
Revised: 09.04.2016

Citation: A. Kudlis, A. I. Sokolov, “Field theory and anisotropy of a cubic ferromagnet near the Curie point”, TMF, 190:2 (2017), 344–353; Theoret. and Math. Phys., 190:2 (2017), 295–302

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Sokolov A.I., Kudlis A., Nikitina M.A., “Effective Potential of the Three-Dimensional Ising Model: the Pseudo-Epsilon Expansion Study”, Nucl. Phys. B, 921 (2017), 225–235  crossref  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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