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

We study the distribution of the complex temperature zeros for the partition function of the Ising model on a Sierpinski gasket using an exact recursive relation. Although the zeros arrange on a curve pinching the real axis at T = 0 in the thermodynamic limit, their density vanishes asymptotically along the curve approaching the origin. This phenomenon explains the coincidence of the low-temperature regime on the Sierpinski gasket and on the linear chain.