Correlation decay and conformal anomaly in the two-dimensional random-bond Ising ferromagnet

TL;DR

This study investigates the decay of correlations and conformal anomaly in the 2D random-bond Ising model, revealing differences in correlation decay rates and confirming theoretical predictions about the conformal anomaly.

Contribution

It provides a numerical analysis of correlation decay and conformal anomaly in the 2D random-bond Ising model, confirming field-theoretical predictions.

Findings

Correlation decay rate differs from direct correlation function evaluation.

Correlation decay matches that of pure systems within error margins.

Conformal anomaly c is estimated to be 1/2, consistent with pure Ising model.

Abstract

The two-dimensional random-bond Ising model is numerically studied on long strips by transfer-matrix methods. It is shown that the rate of decay of correlations at criticality, as derived from averages of the two largest Lyapunov exponents plus conformal invariance arguments, differs from that obtained through direct evaluation of correlation functions. The latter is found to be, within error bars, the same as in pure systems. Our results confirm field-theoretical predictions. The conformal anomaly $c$ is calculated from the leading finite-width correction to the averaged free energy on strips. Estimates thus obtained are consistent with $c=1/2$, the same as for the pure Ising model.