ANISOTROPIC SPIRAL SELF-AVOIDING LOOPS
S. K., Ken‐Yu Lin · International Journal of Modern Physics B · 1988
We have studied two models of anisotropic spiral self-avoiding loops on the square lattice, and developed a semi-numerical method to calculate the number Un of loops with n steps. The asymptotic form of Un appears to be n−1/2μn (n is even) where μ is the connective constant. A special case of these models was considered previously by Lin et al. They required that if the first step is north (south), the closing step cannot be west (east). The asymptotic form of Un in the special case agrees with our general result.