The four-dimensional site-diluted Ising model: A finite-size scaling study (original) (raw)
Related papers
Site-diluted Ising model in four dimensions
Physical Review E, 2009
In the literature, there are five distinct, fragmented sets of analytic predictions for the scaling behaviour at the phase transition in the random-site Ising model in four dimensions. Here, the scaling relations for logarithmic corrections are used to complete the scaling pictures for each set. A numerical approach is then used to confirm the leading scaling picture coming from these predictions and to discriminate between them at the level of logarithmic corrections.
Scaling analysis of the site-diluted Ising model in two dimensions
Physical Review E, 2008
A combination of recent numerical and theoretical advances are applied to analyze the scaling behaviour of the site-diluted Ising model in two dimensions, paying special attention to the implications for multiplicative logarithmic corrections. The analysis focuses primarily on the odd sector of the model (i.e., that associated with magnetic exponents), and in particular on its Lee-Yang zeros, which are determined to high accuracy. Scaling relations are used to connect to the even (thermal) sector, and a first analysis of the density of zeros yields information on the specific heat and its corrections. The analysis is fully supportive of the strong scaling hypothesis and of the scaling relations for logarithmic corrections.
Reexamination of Scaling in the Five-dimensional Ising model
Arxiv preprint cond-mat/ …, 2006
In three dimensions, or more generally, below the upper critical dimension, scaling laws for critical phenomena seem well understood, for both infinite and for finite systems. Above the upper critical dimension of four, finite-size scaling is more difficult.
Ising exponents in the two-dimensional site-diluted Ising model
Journal of Physics A: Mathematical and General, 1997
We study the site-diluted Ising model in two dimensions with Monte Carlo simulations. Using finite-size scaling techniques we compute the critical exponents observing deviations from the pure Ising ones. The differences can be explained as the effects of logarithmic corrections, without requiring to change the Universality Class.
International Journal of Modern Physics C
Corrections to scaling in the 3D Ising model are studied based on nonperturbative analytical arguments and Monte Carlo (MC) simulation data for different lattice sizes [Formula: see text]. Analytical arguments show the existence of corrections with the exponent [Formula: see text], the leading correction-to-scaling exponent being [Formula: see text]. A numerical estimation of [Formula: see text] from the susceptibility data within [Formula: see text] yields [Formula: see text], in agreement with this statement. We reconsider the MC estimation of [Formula: see text] from smaller lattice sizes, [Formula: see text], using different finite-size scaling methods, and show that these sizes are still too small, since no convergence to the same result is observed. In particular, estimates ranging from [Formula: see text] to [Formula: see text] are obtained, using MC data for thermodynamic average quantities, as well as for partition function zeros. However, a trend toward smaller [Formula: s...
Dimensional reduction breakdown and correction to scaling in the random-field Ising model
Physical Review E, 2020
We provide a theoretical analysis by means of the nonperturbative functional renormalization group (NP-FRG) of the corrections to scaling in the critical behavior of the random-field Ising model (RFIM) near the dimension dDR ≈ 5.1 that separates a region where the renormalized theory at the fixed point is supersymmetric and critical scaling satisfies the d → d − 2 dimensional reduction property (d > dDR) from a region where both supersymmetry and dimensional reduction break down at criticality (d < dDR). We show that the NP-FRG results are in very good agreement with recent large-scale lattice simulations of the RFIM in d = 5 and we detail the consequences for the leading correction-to-scaling exponent of the peculiar boundary-layer mechanism by which the dimensional-reduction fixed point disappears and the dimensional-reduction-broken fixed point emerges in dDR.
Physical Review B, 2015
The random-field Ising model shows extreme critical slowdown that has been described by activated dynamic scaling: the characteristic time for the relaxation to equilibrium diverges exponentially with the correlation length, ln τ ∼ ξ ψ /T , with ψ an a priori unknown barrier exponent. Through a nonperturbative functional renormalization group, we show that for spatial dimensions d less than a critical value dDR ≃ 5.1, also associated with dimensional-reduction breakdown, ψ = θ with θ the temperature exponent near the zero-temperature fixed point that controls the critical behavior. For d > dDR on the other hand, ψ = θ − 2λ where θ = 2 and λ > 0 a new exponent. At the upper critical dimension d = 6, λ = 1 so that ψ = 0, and activated scaling gives way to conventional scaling. We give a physical interpretation of the results in terms of collective events in real space, avalanches and droplets. We also propose a way to check the two regimes by computer simulations of long-range 1-d systems.
On the Four-Dimensional Diluted Ising Model
1995
In this letter we show strong numerical evidence that the four dimensional Diluted Ising Model for a large dilution is not described by the Mean Field exponents. These results suggest the existence of a new fixed point with non-gaussian exponents.
Corrections to scaling in the 3D Ising model: A comparison between MC and MCRG results
International Journal of Modern Physics C
Corrections to scaling in the 3D Ising model are studied based on Monte Carlo (MC) simulation results for very large lattices with linear lattice sizes up to [Formula: see text]. Our estimated values of the correction-to-scaling exponent [Formula: see text] tend to decrease below the usually accepted value about 0.83 when the smallest lattice sizes, i.e. [Formula: see text] with [Formula: see text], are discarded from the fits. This behavior apparently confirms some of the known estimates of the Monte Carlo renormalization group (MCRG) method, i.e. [Formula: see text] and [Formula: see text]. We discuss the possibilities that [Formula: see text] is either really smaller than usually expected or these values of [Formula: see text] describe some transient behavior which, eventually, turns into the correct asymptotic behavior at [Formula: see text]. We propose refining MCRG simulations and analysis to resolve this issue. Our actual MC estimations of the critical exponents [Formula: see...
Critical Exponents of the 3-D Ising Model
International Journal of Modern Physics C, 1996
We present a status report on the ongoing analysis of the 3D Ising model with nearest-neighbor interactions using the Monte Carlo Renormalization Group (MCRG) and finite size scaling (FSS) methods on 64364^3643, 1283128^31283, and 2563256^32563 simple cubic lattices. Our MCRG estimates are Knnc=0.221655(1)(1)K_{nn}^c=0.221655(1)(1)Knnc=0.221655(1)(1) and nu=0.625(1)\nu=0.625(1)nu=0.625(1). The FSS results for KcK^cKc are consistent with those from MCRG but the value of nu\nunu is not. Our best estimate eta=0.025(6)\eta = 0.025(6)eta=0.025(6) covers the spread in the MCRG and FSS values. A surprise of our calculation is the estimate omegaapprox0.7\omega \approx 0.7omegaapprox0.7 for the correction-to-scaling exponent. We also present results for the renormalized coupling gRg_RgR along the MCRG flow and argue that the data support the validity of hyperscaling for the 3D Ising model.