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

## TL;DR

This paper precisely enumerates self-avoiding walks on BCC and FCC lattices up to certain lengths, providing accurate estimates of growth constants and critical exponents, and compares these with previous results on cubic lattices.

## Contribution

It introduces an exact enumeration method for BCC and FCC lattices and determines key parameters with high precision, extending the understanding of lattice models.

## Key findings

- Enumerated walks up to length 28 (BCC) and 24 (FCC).
- Provided accurate estimates for growth constants and amplitudes.
- Results agree with previous studies but offer improved precision.

## 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 $D=1.0460(50)$.