Lee-Yang zeros and the Ising model on the Sierpinski gasket

We study the distribution of the complex temperature zeros for the partitio n function of the Ising model on a Sierpinski gasket using an exact recursi ve relation. Although the zeros arrange on a curve pinching the real axis a t T = 0 in the thermodynamic limit, their density vanishes asymptotically a long the curve approaching the origin. This phenomenon explains the coincid ence of the low-temperature regime on the Sierpinski gasket and on the line ar chain.