Exact enumeration of self-avoiding walks on BCC and FCC lattices

Abstract

Self-avoiding walks on the body-centered-cubic (BCC) and face-centered-cubic (FCC) lattices are enumerated up to lengths 28 and 24, respectively, using the length-doubling method. Analysis of the enumeration results yields values for the exponents $\gamma$ and $\nu$ which are in agreement with, but less accurate than those obtained earlier from enumeration results on the simple cubic lattice. The non-universal growth constant and amplitudes are accurately determined, yielding for the BCC lattice $\mu =6.530520(20)$, $A=1.1785(40)$, and $D=1.0864(50)$, and for the FCC lattice $\mu =10.037075(20)$, $A=1.1736(24)$, and $D=1.0460(50)$.

10 pages, 8 figures

References in corpus (4)

• Accurate estimate of the critical exponent $\nu$ for self-avoiding walks via a fast implementation of the pivot algorithm
• High-precision estimate of the hydrodynamic radius for self-avoiding walks
• Scale-free Monte Carlo method for calculating the critical exponent $\gamma$ of self-avoiding walks
• Square lattice self-avoiding walks and biased differential approximants

Cited by in corpus (4)

• Precision calculation of critical exponents in the $O(N)$ universality classes with the nonperturbative renormalization group
• Logarithmic finite-size scaling of the self-avoiding walk at four dimensions
• Asymptotically faster algorithm for counting self-avoiding walks and self-avoiding polygons
• Conformal amplitude hierarchy and the Poincare disk