Determination of the exponent gamma for SAWs on the two-dimensional Manhattan lattice

TL;DR

This study uses Monte Carlo simulations to accurately estimate the critical exponent gamma for self-avoiding walks on a two-dimensional Manhattan lattice, confirming its universal value but revealing complex scaling corrections.

Contribution

It provides a high-precision Monte Carlo estimate of gamma for SAWs on the Manhattan lattice, highlighting non-analytic corrections to scaling not predicted by conformal field theory.

Findings

Gamma estimated as approximately 1.3425(3)

Strong corrections to scaling suggest non-analytic behavior

Results support the universal value 43/32 for gamma

Abstract

We present a high-statistics Monte Carlo determination of the exponent gamma for self-avoiding walks on a Manhattan lattice in two dimensions. A conservative estimate is $\gamma \gtapprox 1.3425(3)$, in agreement with the universal value 43/32 on regular lattices, but in conflict with predictions from conformal field theory and with a recent estimate from exact enumerations. We find strong corrections to scaling that seem to indicate the presence of a non-analytic exponent Delta < 1. If we assume Delta = 11/16 we find gamma = 1.3436(3), where the error is purely statistical.