Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IMPURITY-IMPURITY PAIR CORRELATION FUNCTION AND PARAMAGNETIC-TO-FERROMAGNETIC TRANSITION IN THE RANDOM ISING MODEL

Dmytro Ivaneyko, Bertrand Berche, Yurij V. Holovatch

Published Jan 1, 2007• 1 citation
OpenAlex

Abstract

In this Monte Carlo study we concentrated on the influence of non-magnetic impurities arranged as the lines with random orientation on paramagnetic-to-ferromagnetic phase transition in the 3D Ising model. Special empha-size is given to the long-distance decay of the impurity-impurity pair correlation function. It is shown that for the lattice sizes considered (L=10-96) and for the two different impurity distributions (purely random and mutually avoiding lines) the function is governed by the power law of 1/ra with an universal exponent a≈2. This result sup-ports our findings about the numerical values of the critical exponents governing magnetic phase transition in the 3D Ising model with long-range-correlated disorder.

Related papers

Impurity-impurity pair correlation function and paramagnetic-ferromagnetic phase transition in the random Ising model

Dmytro Ivaneyko, Bertrand Berche, Yurij V. Holovatch +1 more

In this Monte Carlo study we concentrated on the influence of non-magnetic impurities arranged as the lines with random orientation on paramagnetic-to-ferromagnetic phase transition in the 3D Ising model. Special emphasize is given to the long-distance decay of the impurity-impurity pair correlation function. It is shown that for the lattice sizes considered (L=10-96) and for the two different impurity distributions (purely random and mutually avoiding lines) the function is governed by the power law of 1/r^a with an universal exponent a \simeq 2. This result supports our findings about the numerical values of the critical exponents governing magnetic phase transition in the 3D Ising model with long-range-correlated disorder.

arXiv:cond-mat/0611778•Nov 30, 2006•1 citation

Computer simulation of the critical behavior of 3D disordered ising model

V. V. Prudnikov, Pavel Vladimirovich Prudnikov, A. N. Vakilov +1 more

The critical behavior of the disordered ferromagnetic Ising model is studied numerically by the Monte Carlo method in a wide range of variation of concentration of nonmagnetic impurity atoms. The temperature dependences of correlation length and magnetic susceptibility are determined for samples with various spin concentrations and various linear sizes. The finite-size scaling technique is used for obtaining scaling functions for these quantities, which exhibit a universal behavior in the critical region; the critical temperatures and static critical exponents are also determined using scaling corrections. On the basis of variation of the scaling functions and values of critical exponents upon a change in the concentration, the conclusion is drawn concerning the existence of two universal classes of the critical behavior of the diluted Ising model with different characteristics for weakly and strongly disordered systems.

arXiv:0709.1450•Journal of Experimental and Theoretical Physics•Aug 1, 2007•35 citations

Critical behavior of the three-dimensional Ising model with anisotropic bond randomness at the ferromagnetic-paramagnetic transition line

Theodoros Papakonstantinou, Anastasios Malakis

We study the ±J three-dimensional (3D) Ising model with a spatially uniaxial anisotropic bond randomness on the simple cubic lattice. The ±J random exchange is applied on the xy planes, whereas, in the z direction, only a ferromagnetic exchange is used. After sketching the phase diagram and comparing it with the corresponding isotropic case, the system is studied at the ferromagnetic-paramagnetic transition line using parallel tempering and a convenient concentration of antiferromagnetic bonds (p(z)=0;p(xy)=0.176). The numerical data clearly point out a second-order ferromagnetic-paramagnetic phase transition belonging in the same universality class with the 3D random Ising model. The smooth finite-size behavior of the effective exponents, describing the peaks of the logarithmic derivatives of the order parameter, provides an accurate estimate of the critical exponent 1/ν=1.463(3), and a collapse analysis of magnetization data gives an estimate of β/ν=0.516(7). These results are in agreement with previous papers and, in particular, with those of the isotropic ±J three-dimensional Ising model at the ferromagnetic-paramagnetic transition line, indicating the irrelevance of the introduced anisotropy.

arXiv:1208.0883•Physical Review E•Jan 23, 2013•14 citations

Critical behavior of the three-dimensional ±J Ising model at the paramagnetic-ferromagnetic transition line

Martin Hasenbusch B, Francesco Parisen Toldin, Andrea Pelissetto C +1 more

We study the critical behavior of the three-dimensional $\ifmmode\pm\else\textpm\fi{}J$ Ising model [with random-exchange probability $P({J}_{xy})=p\ensuremath{\delta}({J}_{xy}\ensuremath{-}J)+(1\ensuremath{-}p)\ensuremath{\delta}({J}_{xy}+J)$] at the transition line between the paramagnetic and ferromagnetic phases, which extends from $p=1$ to a magnetic-glassy multicritical point at $p={p}_{N}\ensuremath{\approx}0.768$. By a finite-size scaling analysis of Monte Carlo simulations at various values of $p$ in the region ${p}_{N}<p<1$, we provide strong numerical evidence that the critical behavior along the ferromagnetic transition line belongs to the same universality class as the three-dimensional randomly dilute Ising model. We obtain the results $\ensuremath{\nu}=0.682(3)$ and $\ensuremath{\eta}=0.036(2)$ for the critical exponents, which are consistent with the estimates $\ensuremath{\nu}=0.683(2)$ and $\ensuremath{\eta}=0.036(1)$ at the transition of randomly dilute Ising models.

arXiv:0704.0427•Physical Review B•Sep 6, 2007•48 citations

Emergence of the three-dimensional diluted Ising model universality class in a mixture of two magnets

Juan Jesus Ruiz-Lorenzo, M. Dudka, Mariana Krasnytska +1 more

Usually, the impact of structural disorder on the magnetic phase transition in the 3D Ising model is analyzed within the framework of quenched dilution by a nonmagnetic component, where some lattice sites are occupied by Ising spins, while others are nonmagnetic. This kind of quenched dilution, according to the Harris criterion, leads to a change in the critical exponents that govern the asymptotics in the vicinity of the phase transition point. However, the inherent reason for the emergence of a new, random Ising model universality class is not the presence of a nonmagnetic component, but the disorder in structure of spin arrangement. To demonstrate this fact, in this paper we set up extensive Monte Carlo simulations of a random mixture of two Ising-like magnets that differ in spin length s and concentration c. In doing so, we analyze the effect of structural disorder per se without appealing to the presence of a nonmagnetic component. We support our numerical simulations with renormalization group calculations. Our results demonstrate the emergence of the 3D randomly diluted Ising model universality class in a random mixture of two Ising magnets. While the asymptotic critical exponents coincide with those known for the site-diluted 3D Ising model, the effective critical behavior is triggered by parameters s and c. The impact of their interplay is a subject of detailed analysis.

arXiv:2411.16659•Physical review. E•Feb 18, 2025•1 citation

Critical exponents of the Ising model in three dimensions with long-range power-law correlated site disorder: A Monte Carlo study

Stanislav Kazmin, Wolfhard Janke E

The critical behavior of the Ising model in three dimensions on a lattice with site disorder is studied by applying Monte Carlo simulation techniques. Two cases for the site disorder are considered: uncorrelated disorder and long-range correlated disorder with a spatial correlation function that decays according to a power law ${r}^{\ensuremath{-}a}$. The critical exponents $\ensuremath{\beta}$ and $\ensuremath{\gamma}$ as well as updated results for the critical exponent $\ensuremath{\nu}$ and confluent correction exponent $\ensuremath{\omega}$ are provided for a variety of different correlation exponents $a$ and disorder concentrations ${p}_{d}$. The estimation is done by using finite-size scaling analyses and a global fit procedure which combines the results obtained for different concentrations of defects. From the estimated critical exponents, the validity of hyperscaling relations is studied and finally the critical temperatures are provided for different $a$ and ${p}_{d}$.

Physical review. B./Physical review. B•Jun 27, 2022•15 citations
In this Monte Carlo study we concentrated on the influence of non-magnetic impurities arranged as the lines with random orientation on paramagnetic-to-ferromagnetic phase transition in the 3D Ising model. Special empha-size is given to the long-distance decay of the impurity-impurity pair correlation function. It is shown that for the lattice sizes considered (L=10-96) and for the two different impurity distributions (purely random and mutually avoiding lines) the function is governed by the power law of 1/ra with an universal exponent a≈2. This result sup-ports our findings about the numerical values of the critical exponents governing magnetic phase transition in the 3D Ising model with long-range-correlated disorder.
In this Monte Carlo study we concentrated on the influence of non-magnetic impurities arranged as the lines with random orientation on paramagnetic-to-ferromagnetic phase transition in the 3D Ising model. Special emphasize is given to the long-distance decay of the impurity-impurity pair correlation function. It is shown that for the lattice sizes considered (L=10-96) and for the two different impurity distributions (purely random and mutually avoiding lines) the function is governed by the power law of 1/r^a with an universal exponent a \simeq 2. This result supports our findings about the numerical values of the critical exponents governing magnetic phase transition in the 3D Ising model with long-range-correlated disorder.
The critical behavior of the disordered ferromagnetic Ising model is studied numerically by the Monte Carlo method in a wide range of variation of concentration of nonmagnetic impurity atoms. The temperature dependences of correlation length and magnetic susceptibility are determined for samples with various spin concentrations and various linear sizes. The finite-size scaling technique is used for obtaining scaling functions for these quantities, which exhibit a universal behavior in the critical region; the critical temperatures and static critical exponents are also determined using scaling corrections. On the basis of variation of the scaling functions and values of critical exponents upon a change in the concentration, the conclusion is drawn concerning the existence of two universal classes of the critical behavior of the diluted Ising model with different characteristics for weakly and strongly disordered systems.
We study the ±J three-dimensional (3D) Ising model with a spatially uniaxial anisotropic bond randomness on the simple cubic lattice. The ±J random exchange is applied on the xy planes, whereas, in the z direction, only a ferromagnetic exchange is used. After sketching the phase diagram and comparing it with the corresponding isotropic case, the system is studied at the ferromagnetic-paramagnetic transition line using parallel tempering and a convenient concentration of antiferromagnetic bonds (p(z)=0;p(xy)=0.176). The numerical data clearly point out a second-order ferromagnetic-paramagnetic phase transition belonging in the same universality class with the 3D random Ising model. The smooth finite-size behavior of the effective exponents, describing the peaks of the logarithmic derivatives of the order parameter, provides an accurate estimate of the critical exponent 1/ν=1.463(3), and a collapse analysis of magnetization data gives an estimate of β/ν=0.516(7). These results are in agreement with previous papers and, in particular, with those of the isotropic ±J three-dimensional Ising model at the ferromagnetic-paramagnetic transition line, indicating the irrelevance of the introduced anisotropy.
We study the critical behavior of the three-dimensional $\ifmmode\pm\else\textpm\fi{}J$ Ising model [with random-exchange probability $P({J}_{xy})=p\ensuremath{\delta}({J}_{xy}\ensuremath{-}J)+(1\ensuremath{-}p)\ensuremath{\delta}({J}_{xy}+J)$] at the transition line between the paramagnetic and ferromagnetic phases, which extends from p=1p=1p=1 to a magnetic-glassy multicritical point at $p={p}_{N}\ensuremath{\approx}0.768$. By a finite-size scaling analysis of Monte Carlo simulations at various values of ppp in the region pN<p<1{p}_{N}<p<1pN​<p<1, we provide strong numerical evidence that the critical behavior along the ferromagnetic transition line belongs to the same universality class as the three-dimensional randomly dilute Ising model. We obtain the results $\ensuremath{\nu}=0.682(3)$ and $\ensuremath{\eta}=0.036(2)$ for the critical exponents, which are consistent with the estimates $\ensuremath{\nu}=0.683(2)$ and $\ensuremath{\eta}=0.036(1)$ at the transition of randomly dilute Ising models.
Usually, the impact of structural disorder on the magnetic phase transition in the 3D Ising model is analyzed within the framework of quenched dilution by a nonmagnetic component, where some lattice sites are occupied by Ising spins, while others are nonmagnetic. This kind of quenched dilution, according to the Harris criterion, leads to a change in the critical exponents that govern the asymptotics in the vicinity of the phase transition point. However, the inherent reason for the emergence of a new, random Ising model universality class is not the presence of a nonmagnetic component, but the disorder in structure of spin arrangement. To demonstrate this fact, in this paper we set up extensive Monte Carlo simulations of a random mixture of two Ising-like magnets that differ in spin length s and concentration c. In doing so, we analyze the effect of structural disorder per se without appealing to the presence of a nonmagnetic component. We support our numerical simulations with renormalization group calculations. Our results demonstrate the emergence of the 3D randomly diluted Ising model universality class in a random mixture of two Ising magnets. While the asymptotic critical exponents coincide with those known for the site-diluted 3D Ising model, the effective critical behavior is triggered by parameters s and c. The impact of their interplay is a subject of detailed analysis.
The critical behavior of the Ising model in three dimensions on a lattice with site disorder is studied by applying Monte Carlo simulation techniques. Two cases for the site disorder are considered: uncorrelated disorder and long-range correlated disorder with a spatial correlation function that decays according to a power law ${r}^{\ensuremath{-}a}$. The critical exponents $\ensuremath{\beta}$ and $\ensuremath{\gamma}$ as well as updated results for the critical exponent $\ensuremath{\nu}$ and confluent correction exponent $\ensuremath{\omega}$ are provided for a variety of different correlation exponents aaa and disorder concentrations pd{p}_{d}pd​. The estimation is done by using finite-size scaling analyses and a global fit procedure which combines the results obtained for different concentrations of defects. From the estimated critical exponents, the validity of hyperscaling relations is studied and finally the critical temperatures are provided for different aaa and pd{p}_{d}pd​.