Sample-to-sample fluctuations and bond chaos in them-component spin glass

Abstract

We calculate the finite-size scaling of the sample-to-sample fluctuations of the free energy $\ensuremath{\Delta}F$ of the $m$ component vector spin glass in the large-$m$ limit. This is accomplished using a variant of the interpolating Hamiltonian technique which is used to establish a connection between the free energy fluctuations and bond chaos. The calculation of bond chaos then shows that the scaling of the free-energy fluctuations with system size $N$ is $\ensuremath{\Delta}F\ensuremath{\sim}{N}^{\ensuremath{\mu}}$ with $\frac{1}{5}\ensuremath{\le}\ensuremath{\mu}\ensuremath{\le}\frac{3}{10}$, and very likely $\ensuremath{\mu}=\frac{1}{5}$ exactly.