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Spin-pair correlations of the classical Heisenberg ferromagnet above and below the critical point: Results of self-consistent Monte Carlo calculations

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Zeitschrift für Physik

Abstract

The spin-pair correlation functions of the classical Heisenberg ferromagnet with simple cubic lattice have been calculated in the paramagnetic and ferromagnetic temperature range using the self-consistent Monte Carlo method.

The results agree with high-temperature series expansions aboveT c , for low temperatures with spin-wave theory. By two different approaches the divergence of the ferromagnetic homogeneous susceptibility in zero field throughout the ferromagnetic temperature range could be verified.

The functional dependence of the static susceptibilityχ T (k) upon the inverse correlation lengthκ 1 is discussed above and belowT c and a Fourier transform for the explicit dependence of the spin correlations upon correlation length belowT c is given.

According to these results the scaling assumptionv=v′ for the exponents of the correlation length in the critical region is consistent with a divergent ferromagnetic susceptibility.

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Author notes

  1. Heiner Müller-Krumbhaar

    Present address: IBM Zurich Research Laboratory, 8803, Rüschlikon-ZH, Switzerland

Authors and Affiliations

  1. Physik-Department E 14 der Technischen Universität München, Deutschland

    Heiner Müller-Krumbhaar

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  1. Heiner Müller-Krumbhaar
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Additional information

Extract from dissertation, Fakultät für Allgemeine Wissenschaften der Technischen Universität München, May 16, 1973: „Bestimmung kritischer Exponenten am Heisenberg-Ferromagneten mit einem selbstkonsistenten Monte-Carlo-Verfahren“.

I gratefully appreciate helpful discussions with H. Schmidt and K. Binder, and thank P. C. Hohenberg for his valuable comments. The computations were performed with the aid of a grant from the Bundesministerium für Bildung und Wissenschaft.

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Müller-Krumbhaar, H. Spin-pair correlations of the classical Heisenberg ferromagnet above and below the critical point: Results of self-consistent Monte Carlo calculations. Z. Physik 267, 261–270 (1974). https://doi.org/10.1007/BF01669446

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