Self-Averaging, Distribution of Pseudo-Critical Temperatures and Finite Size Scaling in Critical Disordered Systems

Abstract

The distributions $P(X)$ of singular thermodynamic quantities in an ensemble of quenched random samples of linear size $l$ at the critical point $T_c$ are studied by Monte Carlo in two models. Our results confirm predictions of Aharony and Harris based on Renormalization group considerations. For an Ashkin-Teller model with strong but irrelevant bond randomness we find that the relative squared width, $R_X$, of $P(X)$ is weakly self averaging. $R_X\sim l^{\alpha /\nu }$, where $\alpha$ is the specific heat exponent and $\nu$ is the correlation length exponent of the pure model fixed point governing the transition. For the site dilute Ising model on a cubic lattice, known to be governed by a random fixed point, we find that $R_X$ tends to a universal constant independent of the amount of dilution (no self averaging). However this constant is different for canonical and grand canonical disorder. We study the distribution of the pseudo-critical temperatures $T_c(i,l)$ of the ensemble defined as the temperatures of the maximum susceptibility of each sample. We find that its variance scales as $(\delta T_c(l){)}^2\sim l^{-2/\nu }$ and NOT as $\sim l^{-d}.Wefindthat$R_χ$isreducedbyafactorof$\sim 70$withrespectto$R_χ(T_c)$bymeasuring$χ$ofeachsampleat$T_c(i,l)$.Weanalyzecorrelationsbetweenthemagnetizationatcriticality$m_i(T_c,l)$andthepseudo-criticaltemperature$T_c(i,l)$intermsofasampleindependentfinitesizescalingfunctionofasampledependentreducedtemperature$(T-T_c(i,l))/T_c$. This function is found to be universal and to behave similarly to pure systems.

31 pages, 17 figures, submitted to Phys. Rev. E

References in corpus (1)

• Revisiting the Theory of Finite Size Scaling in Disordered Systems: νCan Be Less Than 2/d

Cited by in corpus (75)

• Strong disorder RG approach of random systems
• Disorder-Induced Critical Phenomena in Hysteresis: Numerical Scaling in Three and Higher Dimensions
• Renormalization group study of the two-dimensional random transverse-field Ising model
• Randomly dilute spin models: a six-loop field-theoretic study
• Infinite disorder scaling of random quantum magnets in three and higher dimensions
• Multicritical Points and Crossover Mediating the Strong Violation of Universality: Wang-Landau Determinations in the Random-Bond $d=2$ Blume-Capel model
• Effective and Asymptotic Critical Exponents of Weakly Diluted Quenched Ising Model: 3d Approach Versus ${\epsilon }^{1/2}$-Expansion
• Strong Violation of Critical Phenomena Universality: Wang-Landau Study of the 2d Blume-Capel Model under Bond Randomness
• Bond dilution in the 3D Ising model: a Monte Carlo study
• Lack of self-averaging of the specific heat in the three-dimensional random-field Ising model
• Renormalization group study of random quantum magnets
• Probability-Changing Cluster Algorithm for Potts Models
• The three-dimensional randomly dilute Ising model: Monte Carlo results
• Sample-Dependent Phase Transitions in Disordered Exclusion Models
• Evidence of Intermittent Cascades from Discrete Hierarchical Dissipation in Turbulence
• Critical behavior and entanglement of the random transverse-field Ising model between one and two dimensions
• Percolation thresholds and fractal dimensions for square and cubic lattices with long-range correlated defects
• Random transverse-field Ising chain with long-range interactions
• First-order transition features of the 3D bimodal random-field Ising model
• Finite size scaling in Ising-like systems with quenched random fields: Evidence of hyperscaling violation
• Distribution of pseudo-critical temperatures and lack of self-averaging in disordered Poland-Scheraga models with different loop exponents
• Short-time dynamics and critical behavior of three-dimensional site-diluted Ising model
• Magnetic critical behavior of two-dimensional random-bond Potts ferromagnets in confined geometries
• Universality and multifractal behaviour of spin-spin correlation functions in disordered Potts models
• Disorder Averaging and Finite Size Scaling
• Crossover and self-averaging in the two-dimensional site-diluted Ising model
• Ising model on 3D random lattices: A Monte Carlo study
• Critical behavior of an even offspringed branching and annihilating random walk cellular automaton with spatial disorder
• Finite size effects in critical fiber networks
• Finite-size scaling properties of random transverse-field Ising chains : Comparison between canonical and microcanonical ensembles for the disorder
• Finite-size scaling of pseudo-critical point distributions in the random transverse-field Ising chain
• Predictive power of MCT: Numerics and Finite size scaling for a mean field spin glass
• Dynamic phase transitions in the presence of quenched randomness
• Crossover behavior in three-dimensional dilute spin systems
• Finite-size scaling analysis of the distributions of pseudo-critical temperatures in spin glasses
• Numerical study of the disordered Poland-Scheraga model of DNA denaturation
• Colloid-polymer mixtures in random porous media: Finite size scaling and connected versus disconnected susceptibilities
• Numerical study on a disordered model for DNA denaturation transition
• Critical and tricritical singularities of the three-dimensional random-bond Potts model for large $q$
• Critical behavior of the pure and random-bond two-dimensional triangular Ising ferromagnet
• Random walks and polymers in the presence of quenched disorder
• Universality and universal finite-size scaling functions in four-dimensional Ising spin glasses
• Is small-world network disordered?
• Critical behavior of interfaces in disordered Potts ferromagnets : statistics of free-energy, energy and interfacial adsorption
• Self-Averaging in the Three Dimensional Site Diluted Heisenberg Model at the critical point
• Delocalization transition of the selective interface model: distribution of pseudo-critical temperatures
• Quenched bond dilution in two-dimensional Potts models
• Critical Behavior of the Three-Dimensional Ising model with Anisotropic Bond Randomness at the Ferromagnetic-Paramagnetic Transition Line
• Surface critical behavior of random systems at the ordinary transition
• On the multifractal statistics of the local order parameter at random critical points : application to wetting transitions with disorder
• Critical Behavior and Lack of Self Averaging in the Dynamics of the Random Potts Model in Two Dimensions
• Non-Self Averaging in Autocorrelations for Potts Models on Quenched Random Gravity Graphs
• On the Finite Size Scaling in Disordered Systems
• Fluids with quenched disorder: Scaling of the free energy barrier near critical points
• Strong Disorder Renewal Approach to DNA denaturation and wetting : typical and large deviation properties of the free energy
• Criticality in the randomness-induced second-order phase transition of the triangular Ising antiferromagnet with nearest- and next-nearest-neighbor interactions
• Rounding of first-order phase transitions and optimal cooperation in scale-free networks
• Fluids in porous media: The case of neutral walls
• Itinerant conductance in fuse-antifuse networks
• Random cascade models of multifractality : real-space renormalization and travelling-waves
• Nematics with quenched disorder : violation of self-averaging
• Three-dimensional Ising model confined in low-porosity aerogels: a Monte Carlo study
• Supersolid Phase in the Diluted Holstein Model
• Correlation functions in the two-dimensional random-field Ising model
• Full reduction of large finite random Ising systems by RSRG
• Numerical evidence of a super-universality of the 2D and 3D random quantum Potts models
• Finite size scaling for the Many-Body-Localization Transition : finite-size-pseudo-critical points of individual eigenstates
• Random wetting transition on the Cayley tree : a disordered first-order transition with two correlation length exponents
• Numerical study of DNA denaturation with self-avoidance: pseudo-critical temperatures and finite size behaviour
• Emergent universal critical behavior of the 2D $N$-color Ashkin-Teller model in the presence of correlated disorder
• Probability distribution of persistent spins in a Ising chain
• Dynamical Critical Properties of the Random-Bond three-state Potts Model
• Dynamical real-space renormalization group calculations with a new clustering scheme on random networks
• Non-self-averaging topological Anderson insulator
• Two-dimensional Site-Bond Percolation as an Example of Self-Averaging System