# The distribution function of the effective fields and the free energy of the ±J random Ising model on the Bethe latticeベーテ格子上の±Jランダムイジングモデルにおける有効場の分布関数と自由エネルギー

## 書誌事項

タイトル

The distribution function of the effective fields and the free energy of the ±J random Ising model on the Bethe lattice

タイトル別名

ベーテ格子上の±Jランダムイジングモデルにおける有効場の分布関数と自由エネルギー

セイノ, ミツヒロ

1993-01-27

## 目次

1. Contents / p5 (0008.jp2)
2. Abstract / p1 (0004.jp2)
3. Zusammenfasung / p2 (0005.jp2)
4. Acknowledgements / p3 (0006.jp2)
5. List of Symbols / p4 (0007.jp2)
6. 1 Introduction / p1 (0010.jp2)
7. 1.1 Ising model / p1 (0010.jp2)
8. 1.2 The density matrix and the Bethe lattice / p2 (0011.jp2)
9. 1.3 Spin glass / p6 (0015.jp2)
10. 1.4 The method of the integral equation for the distribution of the effective field for the random Ising model / p7 (0016.jp2)
11. 1.5 The outline of present paper / p11 (0020.jp2)
12. 2 The symmetric continuous distribution function for the coordination number z=4,5,and 6 / p15 (0024.jp2)
13. 2.1 The algebraic equations for general z / p16 (0025.jp2)
14. 2.2 The solution of the simultaneous algebraic equation for z=4,5,and 6 / p18 (0027.jp2)
15. 2.3 Summary and discussion / p20 (0029.jp2)
16. 3 The asymmetric continuous distribution function of z=3 for the concentration p / p22 (0031.jp2)
17. 3.1 The equation with the solution of the symmetric and asymmetric distribution for general z / p22 (0031.jp2)
18. 3.2 The solution of the equation for z=3 / p24 (0033.jp2)
19. 4 The free energy of the spin glass with the continuous distribution of the effective field at T=0 / p27 (0036.jp2)
20. 4.1 The calculation of the one-body free energy / p28 (0037.jp2)
21. 4.2 The calculation of the two-body free energy / p29 (0038.jp2)
22. 4.3 The free energy for z=3,4,5,6, and ∞ / p30 (0039.jp2)
23. 5 The free energy of the Ising spin glass on the Bethe lattice at finite temperature / p36 (0045.jp2)
24. 5.1 The free energy in terms of S(x) / p36 (0045.jp2)
25. 5.2 Free energies of the ferro-,antiferro-,and paramagnetic states / p39 (0048.jp2)
26. 5.3 Spin glass state of the ±J model / p40 (0049.jp2)
27. 6 Integral kernel of the spin glass integral equation for the Bethe lattice / p42 (0051.jp2)
28. 6.1 Calculation of the integral kernel K(x,y) / p42 (0051.jp2)
29. 6.2 The kernel K(x,y) at zero temperature / p44 (0053.jp2)
30. Conclusion / p47 (0056.jp2)
31. Appendices / p48 (0057.jp2)
32. Appendix A Definite integrals of products of Bessel function / p48 (0057.jp2)
33. Appendix B Tables of the integral of products of Bessel functions / p51 (0060.jp2)
34. Appendix C The simultaneous algebraic equations with a symmetric distribution for (i) z=3, (ii) z=4, (iii) z=5 and (iv) z=6 and with an asymmetric distribution for (v) z=3 / p54 (0063.jp2)
35. Appendix D The equations for (i) f₁(a)=0, (ii) b=f₂(a), (iii) d₀=f(a), (iv) d₀=f₃(a), (iv)d₂=f₄(a) / p59 (0068.jp2)
36. Appendix E List of formulas / p61 (0070.jp2)
37. References / p62 (0071.jp2)
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## 各種コード

• NII論文ID(NAID)
500000094969
• NII著者ID(NRID)
• 8000000095195
• DOI(NDL)
• NDL書誌ID
• 000000259283
• データ提供元
• NDL-OPAC
• NDLデジタルコレクション

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