Universality class of 3D site-diluted and bond-diluted Ising systems

Abstract

We present a finite-size scaling analysis of high-statistics Monte Carlo simulations of the three-dimensional randomly site-diluted and bond-diluted Ising model. The critical behavior of these systems is affected by slowly-decaying scaling corrections which make the accurate determination of their universal asymptotic behavior quite hard, requiring an effective control of the scaling corrections. For this purpose we exploit improved Hamiltonians, for which the leading scaling corrections are suppressed for any thermodynamic quantity, and improved observables, for which the leading scaling corrections are suppressed for any model belonging to the same universality class. The results of the finite-size scaling analysis provide strong numerical evidence that phase transitions in three-dimensional randomly site-diluted and bond-diluted Ising models belong to the same randomly dilute Ising universality class. We obtain accurate estimates of the critical exponents, $\nu =0.683(2)$, $\eta =0.036(1)$, $\alpha =-0.049(6)$, $\gamma =1.341(4)$, $\beta =0.354(1)$, $\delta =4.792(6)$, and of the leading and next-to-leading correction-to-scaling exponents, $\omega =0.33(3)$ and ${\omega }_2=0.82(8)$.

45 pages, 22 figs, revised estimate of nu

References in corpus (4)

• The critical exponents of the superfluid transition in He4
• Multicritical behavior in the fully frustrated XY model and related systems
• Universality class of 3D site-diluted and bond-diluted Ising systems
• High-temperature series for the bond-diluted Ising model in 3, 4 and 5 dimensions

Cited by in corpus (51)

• A Finite Size Scaling Study of Lattice Models in the three-dimensional Ising Universality Class
• Fermionic quantum criticality in honeycomb and $\pi$-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
• Anisotropic perturbations in three-dimensional O(N)-symmetric vector models
• The critical behavior of three-dimensional Ising spin glass models
• Monte Carlo study of an improved clock model in three dimensions
• High-precision estimate of the hydrodynamic radius for self-avoiding walks
• Boundary critical behavior of the three-dimensional Heisenberg universality class
• Universality class of 3D site-diluted and bond-diluted Ising systems
• Monte Carlo study of a generalized icosahedral model on the simple cubic lattice
• Scale-free Monte Carlo method for calculating the critical exponent $\gamma$ of self-avoiding walks
• Strong-disorder paramagnetic-ferromagnetic fixed point in the square-lattice +- J Ising model
• Multicritical Nishimori point in the phase diagram of the +- J Ising model on a square lattice
• The dynamic critical exponent $z$ of the three-dimensional Ising universality class: Monte Carlo simulations of the improved Blume-Capel model
• Restoring isotropy in a three-dimensional lattice model: The Ising universality class
• Magnetic-glassy multicritical behavior of the three-dimensional +- J Ising model
• Ferromagnetic-glassy transitions in three-dimensional Ising spin glasses
• Universality in disordered systems: The case of the three-dimensional random-bond Ising model
• Relaxational dynamics in 3D randomly diluted Ising models
• Griffiths phase and critical behavior of the 2D Potts models with long-range correlated disorder
• Ordered magnetism in the intrinsically decorated $j{}_{\mathrm{eff}}$ = $\frac{1}{2}$ $\alpha$-CoV${}_3$O${}_8$
• Critical Casimir force in the presence of random local adsorption preference
• Self-Averaging in the Three Dimensional Site Diluted Heisenberg Model at the critical point
• Critical Behavior of the Three-Dimensional Ising model with Anisotropic Bond Randomness at the Ferromagnetic-Paramagnetic Transition Line
• Wang-Landau study of the 3D Ising model with bond disorder
• Super slowing down in the bond-diluted Ising model
• Critical behavior of weakly disordered Ising model: Six-loop $\sqrt{\epsilon }$ expansion study
• The three-dimensional gauge-glass model
• Fluids in porous media: The case of neutral walls
• The ordinary surface universality class of the three-dimensional O($N$) model
• Critical exponent $\nu$ of the Ising model in three dimensions with long-range correlated site disorder analyzed with Monte Carlo techniques
• The Site-Diluted Ising Model in Four Dimension
• Magnetic properties and critical behavior of disordered Fe_{1-x}Ru_x alloys: a Monte Carlo approach
• Finite-Size Scaling at fixed Renormalization-Group invariant
• Improvement of Monte Carlo estimates with covariance-optimized finite-size scaling at fixed phenomenological coupling
• Fluid-fluid demixing curves for colloid-polymer mixtures in a random colloidal matrix
• A comparison of cluster algorithms for the bond-diluted Ising model
• Cluster percolation in the three-dimensional $\pm J$ random-bond Ising model
• Phase transitions and continuously variable scaling in a chiral quenched disordered model
• Critical behavior of the Ising model on square-triangle tilings
• Surface critical behavior of the three-dimensional O(3) model
• Multiscaling in the 3D critical site-diluted Ising ferromagnet
• Inhomogeneities on all scales at a phase transition altered by disorder
• Conjecture on the lower bound of the length-scale critical exponent $\nu$ at continuous phase transitions
• Intrinsic Heralding and Optimal Decoders for Non-Abelian Topological Order
• Emergence of the 3D diluted Ising model universality class in a mixture of two magnets
• Equilibrium and out-of-equilibrium critical dynamics of the three-dimensional Heisenberg model with random cubic anisotropy
• Finite-temperature topological transitions in the presence of quenched uncorrelated disorder
• Dynamical Critical Properties of the Random-Bond three-state Potts Model
• Temperature scaling analysis of the 3D disordered Ising model with power-law correlated defects
• Effects of quenched disorder in three-dimensional lattice ${\mathbb{Z}}_2$ gauge Higgs models
• Off-Diagonal dipolar interactions in the mixed Ising--XY magnet $LiH{o}_{x}E{r}_{1-x}{F}_4$