Transverse size of interacting directed lattice animals studied by Yang–Lee approach

Abstract

Distributions of zeros of the grand canonical partition function in the complex fugacity plane are examined numerically for a model of self interacting directed lattice animals on infinite strips of the square lattice. It is shown that patterns of these zeros have a simple circular-like forms for large values of the interaction strength, with a small fraction of points scattered over the plane. As the interaction weakens, the zeros make up a more complicated structure which consists of a large number of branches. For weak interaction strength, the zeros lying closest to the real axis approach it by following the power-law behavior as the function of strip width. This allowed us to get quite good estimate of transverse size critical exponent for animals in the swollen state as well as at the point of their collapse transition. For stronger interactions, we found that these zeros move much faster toward the real axis—following an exponential law, which leads us to conjecture that animal transverse size diverges in a logarithmic way in the thermodynamic limit. An additional analysis, based on finite-size scaling analysis of the animal longitudinal correlation length, supports this conjecture.