田﨑 晴明

Classical ferromagnetic spin systems on self-similar fractal lattices are studied. By a variation of Simon's argument (1980), it is shown rigorously that the critical decay exponent Delta (which is characterised by ( phi x phi y)&lt or approximately=dist(x,y) at the critical point) satisfies the bound Delta &lt or=Q, where Q is the connectivity. The author also discusses some general features of the phase transitions and critical phenomena.

In the d-dimensional ferromagnetic Ising and φ4 systems, the motion of the first Lee-Yang zero when the lattice size tends to infinity is studied. In particular, a power law behavior at the critical point, which is distinct from those in noncritical points, is elucidated. © 1987 American Institute of Physics.

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. Therefore, random surfaces collapse into branched polymers in the scaling limit. © 1985.