2016/11/30 by Victor Dotsenko, Yurij Holovatch, Maxym Dudka +2
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Condensed matter physics #Ferromagnetism #Gaussian #Internal energy #Ising model #Lattice (music) #Mathematics #Physics #Probability distribution #Quantum mechanics #Renormalization #Renormalization group #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Thermodynamics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.95.032118
published as Phys. Rev. E 95, 032118 (2017) · 12 pages, accepted version
arxiv created 2017/02/10 · openalex publication_date 2017/03/08 · arxiv updated 2017/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 ∼Llnln(L). In contrast, the specific heat is shown to be self-averaging with a distribution function that tends to a δ peak in the thermodynamic limit L→∞. 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.