Universality from disorder in the random-bond Blume-Capel model

Abstract

Using high-precision Monte Carlo simulations and finite-size scaling we study the effect of quenched disorder in the exchange couplings on the Blume-Capel model on the square lattice. The first-order transition for large crystal-field coupling is softened to become continuous, with a divergent correlation length. An analysis of the scaling of the correlation length as well as the susceptibility and specific heat reveals that it belongs to the universality class of the Ising model with additional logarithmic corrections which is also observed for the Ising model itself if coupled to weak disorder. While the leading scaling behavior of the disordered system is therefore identical between the second-order and first-order segments of the phase diagram of the pure model, the finite-size scaling in the ex-first-order regime is affected by strong transient effects with a crossover length scale L^{*}≈32 for the chosen parameters.

Monte Carlo study of the interfacial adsorption of the Blume-Capel model

“…Finally, it is worth noting that the finite-size scaling behavior of both [W ] L and R [W ] L is affected by strong transient effects with a crossover length-scale L * ≈ 32, where a turnaround in the behavior sets off. This is consistent with previous observations on the scaling behavior of the correlation length and other thermodynamic observables of the system for the same range of parameters [39]. Indeed, in Ref.…”

“…Indeed, in Ref. [39] it has been explicitly shown that L ≈ 32 is the apparent size where the first-order characteristic signatures of the transition disappear. Of course, we expect that the value of L * depends on the disorder strength r as well as on the strength of the first-order transition and it would be interesting to investigate the shift of this crossover length-scale as a function of ∆ and r. However this is a task that goes beyond the scope of the present work.…”

Deep learning on the 2-dimensional Ising model to extract the crossover region with a variational autoencoder

“…Additionally, the Kondo Effect is important in certain metallic compounds with dilute concentrations of magnetic impurities that cross over from a weakly-coupled Fermi liquid phase to a local Fermi liquid phase upon reducing the temperature below some threshold 39 . Furthermore, examples of strong crossover phenomena have also been recently discovered in classical models of statistical mechanics such as the Blume-Capel model and the random-field Ising model 40,41 .…”

Metastable behavior of the spin-s Ising and Blume-Capel ferromagnets: A Monte Carlo study

“…For an extensive discussion on the Blume-Capel model, including the phase diagram and its critical properties we refer the reader to Ref. [12][13][14][15].…”