Abstracts of papers by Takashi Hara (Part I)

10. Hal Tasaki and Takashi Hara.
    Critical behaviour in a system of branched polymers.
    Prog. Theor. Phys. Suppl. 92 (1987) 14--25.

    ABSTRACT:
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9. Takashi Hara and Hal Tasaki.
   Rigorous renormalization group analysis of φ⁴ field theory.
   Prog. Theor. Phys. Suppl. 92 (1987) 26--45.

   ABSTRACT:
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8. Kei-ichi Kondo and Takashi Hara.
   Critical exponent of susceptibility in d > 4 dimensions. for a class of general ferromagnets
   J. Stat. Phys. 28 (1987) 1206--1208.

   ABSTRACT:
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7. Takashi Hara and Hal Tasaki.
   A rigorous control of logarithmic correction in four dimensional φ⁴ spin systems. II. critical behavior of susceptibility and correlation length.
   J. Stat. Phys. 47 (1987) 99-121.

   ABSTRACT: Continuing the analysis started in Part I of this work, we investigate critical phenomena in weakly coupled φ⁴ spin systems in four dimensions. Concerning the critical behaviour of the susceptibility and the correlation length (in the high-temperature phase), the existence of logarithmic corrections to their mean-field type behaviour is rigorously shown (i.e., we prove χ(t) \sim t^-1 | log t |^1/3, ξ(t) \sim t^-1/2 |log t|^1/6).
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6. Takashi Hara.
   A rigorous control of logarithmic corrections in four dimensional φ⁴ spin systems. I. Trajectory of effective Hamiltonians.
   J. Stat. Phys. 47 (1987) 57-98.

   ABSTRACT: Using Gawedzki and Kupianen's rigorous block spin transformation method, we study critical phenomena in φ⁴ spin systems in four dimensions. In this Part I of our study, we investigate in detail the renormalization group trajectory of the system not exactly at the critical point.
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5. Hal Tasaki and Takashi Hara.
   Collapse of random surfaces in connected plaquette model.
   Phys. Lett. 112A (1985) 115--118.

   ABSTRACT: Critical phenomena in a simple stochastic geometric model of random surfaces are studied. We find that, at the critical point, the characteristic area remains finite while the susceptibility diverges. Therfore, random surfaces collapse into branched polymers in the scaling limit.
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4. Takashi Hara.
   Construction of a nontrivial field theory in 3 dimensions starting from a Lagrangian of φ⁶-type.
   Prog. Theor. Phys. 76 (1986) 318--320.

   ABSTRACT:
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3. Takashi Hara, Tetsuya Hattori and Hal Tasaki
   Skeleton inequalities and mean field properties for lattice spin systems.
   J. Statist. Phys. 26 (1985) 2922--2929.

   ABSTRACT:
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2. Hal Tasaki and Takashi Hara.
   Mean field bound and GHS inequality.
   J. Statist. Phys.35 (1984), 99--107.

   ABSTRACT:
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1. Takashi Hara and Hal Tasaki.
   Fisher's inequality revisited.
   Physics Letters, 100A (1984) 166--169.

   ABSTRACT: Under some appropriate assumptions, we give a simple and unified proof of the relations among the critical exponents of χ and ν_φ in Ising and φ⁴-like ferromagnets: (2-η) ν_φ \geq γ, (2-η) μ_φ \geq 1 - 1/δ (where φ \geq φ_c, φ\neq 0); (2-η) ν_{φ_c} = γ, (2-η) μ_{φ_c} = 1 - δ, where φ_c = η/2-1; and 2 ν |_φ \geq γ| (φ \geq -1, φ \neq 0).
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Conference Proceedings:

2. Takashi Hara and Gordon Slade.
   Mean-field behaviour and the lace expansion.
   In Probability and Phase Transition, Proceedings of the NATO ASI on Random Spatial Processes, Cambridge, 1993. G.R. Grimmett ed. , Kluwer (1994).
1. Takashi Hara and Gordon Slade.
   The mean-field critical behaviour of percolation in high dimensions.
   In Mathematical Physics, Proceedings of the IXth International Congres on Mathematical Physics, Swansea, 1988. B. Simon, A. Truman, I. M. Davies eds. , Adam-Hilger (1989).