The self-avoiding walk on the honeycomb lattice

Abstract

The author analyses the chain generating function for the self-avoiding walk problem on the honeycomb lattice. She uses the exact critical point value of Nienhuis and finds exponent values of gamma approximately 1.344 and Delta ₁ approximately 0.93 for the dominant and first confluent exponents. The former value is in agreement with Nienhuis' exact result. Second and third confluent exponents, Delta ₂ approximately 1.2 and Delta ₃ approximately 1.5, are also identified, these exponents being consistent with Monte Carlo results and Nienhuis' exact irrelevant eigenvalue, respectively.