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Prog. Theor. Phys. Vol. 46 No. 4 (1971) pp. 1054-1070

[ Full Text PDF : FREE ACCESS (870K) ]

Scaling with a Parameter in Spin Systems near the Critical Point. I

Masuo Suzuki

Institute of Solid State Physics, University of Tokyo, Roppongi, Minato-ku, Tokyo

(Received April 26, 1971)

Abstract:

The Hamiltonian of the form H=H0+λH1 is discussed, where λ is a parameter to change symmetry, dimensionality, or potential range. Scaling with the parameter λ is studied for thermodynamic quantities such as the free energy. By assuming the scaled form F(ε,λ)=ε2-αF(λ/εφ) for the singular part of the free energy near the critical point Tc(ε=(T-Tc)/Tc), the expression (or explicit value) of the critical exponent φ is obtained in each case of change of symmetry, dimensionality and potential range. In particular, the universal relation φ=γ is found for change of dimensionality, where γ is the critical exponent of the susceptibility in the unperturbed Hamiltonian H0. An extension to dynamical critical phenomena is also discussed briefly, particularly in connection with the critical slowing down. A possibility is suggested to derive this generalized scaling with the parameter λ by applying the usual scaling law to each term of the perturbational expansion with respect to the parameter λ.


URL : http://ptp.ipap.jp/link?PTP/46/1054/
DOI : 10.1143/PTP.46.1054

[ Full Text PDF : FREE ACCESS (870K) ] Citation:

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Citing Article(s) :

  1. Journal of the Physical Society of Japan 66 (1997) pp. 3053-3062 :
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  2. Progress of Theoretical Physics Vol. 49 No. 5 (1973) pp. 1451-1458 :
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  3. Progress of Theoretical Physics Vol. 56 No. 3 (1976) pp. 1007-1008 :
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  4. Progress of Theoretical Physics Vol. 56 No. 5 (1976) pp. 1454-1469 :
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  5. Progress of Theoretical Physics Vol. 58 No. 4 (1977) pp. 1142-1150 :
    Static and Dynamic Finite-Size Scaling Theory Based on the Renormalization Group Approach
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  6. Progress of Theoretical Physics Vol. 75 No. 5 (1986) pp. 1066-1075 :
    Study on the Critical Properties of the One-Dimensional Quantum XXZ Model with General Spin S Using the Quantum Renormalization Group Method
    Makoto Inoue and Masuo Suzuki

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