Self-averaging in the random 2D Ising ferromagnet

Abstract

We study sample-to-sample fluctuations in a critical two-dimensional Ising model with quenched random ferromagnetic couplings. Using replica calculations in the renormalization group framework we derive explicit expressions for the probability distribution function of the critical internal energy and for the specific heat fluctuations. It is shown that the disorder distribution of internal energies is Gaussian, and the typical sample-to-sample fluctuations as well as the average value scale with the system size $L$ like $\sim L\ln \ln (L)$. In contrast, the specific heat is shown to be self-averaging with a distribution function that tends to a $\delta$-peak in the thermodynamic limit $L\to \infty$. While previously a lack of self-averaging was found for the free energy, we here obtain results for quantities that are directly measurable in simulations, and implications for measurements in the actual lattice system are discussed.

12 pages, accepted version

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Cited by in corpus (5)

• Universality from disorder in the random-bond Blume-Capel model
• Domain-wall excitations in the two-dimensional Ising spin glass
• Ising universality in the two-dimensional Blume-Capel model with quenched random crystal field
• Properties of the Superfluid in the Disordered Bose-Hubbard Model
• Lack of self-averaging of the critical internal energy in a weakly-disordered Baxter model