Sample-to-sample fluctuations and bond chaos in the $m$-component spin glass

Abstract

We calculate the finite size scaling of the sample-to-sample fluctuations of the free energy $\Delta F$ 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 fluctuaions with system size $N$ is $\Delta F\sim N^{\mu }$ with $1/5\le \mu <3/10$, and very likely $\mu =15$ exactly.

12 pages, 1 figure

References in corpus (8)

• Extreme value problems in Random Matrix Theory and other disordered systems
• Finite size corrections in the Sherrington-Kirkpatrick model
• Free energy fluctuations and chaos in the Sherrington-Kirkpatrick model
• Large Deviations of the Free-Energy in Diluted Mean-Field Spin-Glass
• Generalised Bose-Einstein phase transition in large-$m$ component spin glasses
• Bond chaos in the Sherrington-Kirkpatrick model
• An exact relation between free energy fluctuations and bond chaos in the Sherrington-Kirkpatrick model
• The m-component spin glass on a Bethe lattice

Cited by in corpus (2)

• Simulations of Ground State Fluctuations in Mean-Field Ising Spin Glasses
• One-dimensional infinite component vector spin glass with long-range interactions