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

理论物理通讯：英文版

Critical Behavior of Ising Model with Long Range Correlated Quenched Impurities

CHENYuan, Yuan

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

The theoretic renormalization-group approach is applied to the study of the critical behavior of the ddimensional Ising model with long-range correlated quenched impurities, which has a power-like correlations r-(d-ρ).The asymptotic scaling law is studied in the framework of the expansion in e = 4 - d. In d ＜ 4, the dynamic exponent z .is calculated up to the second order in ρ with ρ = O(e1/2). The shape function is obtained in one-loop calculation.When d = 4, the logarithmic corrections to the critical behavior are found. The finite size effect on the order parameter relaxation rate is also studied.

Related papers

Critical Behavior of Ising Model with Long Range Correlated Quenched Impurities

Yuan Chen

The theoretic renormalization-group approach is applied to the study of the critical behavior of the -dimensional Ising model with long-range correlated quenched impurities, which has a power-like correlations . The asymptotic scaling law is studied in the framework of the expansion in . In , the dynamic exponent is calculated up to the second order in with . The shape function is obtained in one-loop calculation. When , the logarithmic corrections to the critical behavior are found. The finite size effect on the order parameter relaxation rate is also studied.

Communications in Theoretical Physics•Jul 15, 2004•0 citations

Dynamics of Non—interacting System with Long—Range Correlated Quenched Impurities

CHENYuan

The theoretic renormalization group approach is applied to the study of the critical behavior of non-interacting system with long-range correlated quenched impurities, which has a power-like correlations r-(d-ρ). Totwo-loop order, the asymptotic scaling laws and the critical exponents are studied in the frame of a double (e, ρ)expansion with ρ of order e = 4 - d. In d ＜ 4, it is argued that the initial slip exponent θ = 0 together with the dynamicexponent z ＜ 2 is exact in this kind of random system.

理论物理通讯：英文版•Jan 1, 2003•0 citations

Short-Time Critical Behavior of Systems with Random Impurities

Y. Chen, Shuo-Hong Guo, Zhibing Li

The theoretical renormalization-group approach is applied to the study of the short-time critical behavior of the Ginzburg-Landau model with long-range random impurities which have a power-like correlation r—(d—ρ. The system initially at a high temperature is firstly quenched to the critical temperature Tc and then released to an evolution with a model A dynamics. The asymptotic scaling laws are studied in the frame of a double expansion in ϵ = 4 — d and δ = ϵ + ρ with δ of the order of ϵ. The initial slip exponent θ′ for the order parameter is calculated up to the first order in ϵ = 4 — d or in ϵ1/2 corresponding to different fixed points, respectively. For d > 4, the short-time behavior of the order parameter is investigated in one loop. Two different logarithmic and exponential-logarithmic corrections to short-time behaviors of both the autocorrelation and the order parameter are also solved in d = 4 dimension. Crossover between the nonrandom behavior and quenched behavior is found for n = 4 (where n is the spin dimensionality) in d = 4 dimension.

physica status solidi (b)•Feb 1, 2001•4 citations

Dynamics of Non-interacting System with Long-Range Correlated Quenched Impurities

Yuan Chen

The theoretic renormalization group approach is applied to the study of the critical behavior of non-interacting system with long-range correlated quenched impurities, which has a power-like correlations . To two-loop order, the asymptotic scaling laws and the critical exponents are studied in the frame of a double expansion with ρ of order . In , it is argued that the initial slip exponent θ = 0 together with the dynamic exponent is exact in this kind of random system.

Communications in Theoretical Physics•Jun 15, 2003•0 citations

Short-time dynamics of spin systems with long-range correlated quenched impurities

Yuan Chen, Zhibing Li

The theoretic renormalization-group approach is applied to the study of short-time critical behavior of the $d$-dimensional spin systems (model A) in the presence of quenched impurities with a long-range correlations decaying as ${r}^{\ensuremath{-}(d\ensuremath{-}\ensuremath{\rho})}$. The asymptotic scaling laws are studied in the frame of a double expansion in $ϵ=4\ensuremath{-}d$ and $\ensuremath{\rho}$ with $\ensuremath{\rho}$ of order $ϵ$. In $d<4$, the initial slip exponents ${\ensuremath{\theta}}^{\ensuremath{'}}$ of the magnetization and $\ensuremath{\theta}$ of the response function, are calculated up to two-loop order. The crossover between fixed points is obtained. The long-time limit of the fluctuation-dissipation ratio is found in the aging regime, and its connection to equilibrium quantities is discussed. The comparison of our results with those of other systems without long-range correlated quenched impurities is also investigated.

Physical Review B•May 27, 2005•15 citations

SHORT-TIME CRITICAL BEHAVIOR OF THE GINZBURG–LANDAU MODEL WITH QUENCHED DISORDER

Zhibing Li, Y. Chen, Shuo-Hong Guo

The theoretic renormalization-group approach is applied to the study of short-time dynamics of the d-dimensional n-component spin systems with long-range interactions r-(d+σ) and quenched disorder which has long-range correlations r-(d-ρ). Asymptotic scaling laws are obtained in a frame of double expansions in ∊=2σ-d and ρ with ρ of the order ∊. The static exponents are obtained exactly to all the order. The initial slip exponents θ′ for the order parameter and θ for the response function, as well as the dynamic exponent z, are calculated upto the first order in ∊. In d=2σ, in contrast to the unique logarithmic decay in the long-time regime which does not depend on σ, ρ, n and the disorder, we find rich scaling structures including logarithmic and exponential-logarithmic scalings in the short-time regime. Non-universal critical scalings of Ising systems are also discussed for d=2σ.

Modern Physics Letters B•Jan 30, 2001•2 citations
The theoretic renormalization-group approach is applied to the study of the critical behavior of the ddimensional Ising model with long-range correlated quenched impurities, which has a power-like correlations r-(d-ρ).The asymptotic scaling law is studied in the framework of the expansion in e = 4 - d. In d ＜ 4, the dynamic exponent z .is calculated up to the second order in ρ with ρ = O(e1/2). The shape function is obtained in one-loop calculation.When d = 4, the logarithmic corrections to the critical behavior are found. The finite size effect on the order parameter relaxation rate is also studied.
The theoretic renormalization-group approach is applied to the study of the critical behavior of the -dimensional Ising model with long-range correlated quenched impurities, which has a power-like correlations . The asymptotic scaling law is studied in the framework of the expansion in . In , the dynamic exponent is calculated up to the second order in with . The shape function is obtained in one-loop calculation. When , the logarithmic corrections to the critical behavior are found. The finite size effect on the order parameter relaxation rate is also studied.
The theoretic renormalization group approach is applied to the study of the critical behavior of non-interacting system with long-range correlated quenched impurities, which has a power-like correlations r-(d-ρ). Totwo-loop order, the asymptotic scaling laws and the critical exponents are studied in the frame of a double (e, ρ)expansion with ρ of order e = 4 - d. In d ＜ 4, it is argued that the initial slip exponent θ = 0 together with the dynamicexponent z ＜ 2 is exact in this kind of random system.
The theoretical renormalization-group approach is applied to the study of the short-time critical behavior of the Ginzburg-Landau model with long-range random impurities which have a power-like correlation r—(d—ρ. The system initially at a high temperature is firstly quenched to the critical temperature Tc and then released to an evolution with a model A dynamics. The asymptotic scaling laws are studied in the frame of a double expansion in ϵ = 4 — d and δ = ϵ + ρ with δ of the order of ϵ. The initial slip exponent θ′ for the order parameter is calculated up to the first order in ϵ = 4 — d or in ϵ1/2 corresponding to different fixed points, respectively. For d > 4, the short-time behavior of the order parameter is investigated in one loop. Two different logarithmic and exponential-logarithmic corrections to short-time behaviors of both the autocorrelation and the order parameter are also solved in d = 4 dimension. Crossover between the nonrandom behavior and quenched behavior is found for n = 4 (where n is the spin dimensionality) in d = 4 dimension.
The theoretic renormalization-group approach is applied to the study of short-time critical behavior of the ddd-dimensional spin systems (model A) in the presence of quenched impurities with a long-range correlations decaying as ${r}^{\ensuremath{-}(d\ensuremath{-}\ensuremath{\rho})}$. The asymptotic scaling laws are studied in the frame of a double expansion in $ϵ=4\ensuremath{-}d$ and $\ensuremath{\rho}$ with $\ensuremath{\rho}$ of order ϵϵϵ. In d<4d<4d<4, the initial slip exponents ${\ensuremath{\theta}}^{\ensuremath{'}}$ of the magnetization and $\ensuremath{\theta}$ of the response function, are calculated up to two-loop order. The crossover between fixed points is obtained. The long-time limit of the fluctuation-dissipation ratio is found in the aging regime, and its connection to equilibrium quantities is discussed. The comparison of our results with those of other systems without long-range correlated quenched impurities is also investigated.
The theoretic renormalization-group approach is applied to the study of short-time dynamics of the d-dimensional n-component spin systems with long-range interactions r-(d+σ) and quenched disorder which has long-range correlations r-(d-ρ). Asymptotic scaling laws are obtained in a frame of double expansions in ∊=2σ-d and ρ with ρ of the order ∊. The static exponents are obtained exactly to all the order. The initial slip exponents θ′ for the order parameter and θ for the response function, as well as the dynamic exponent z, are calculated upto the first order in ∊. In d=2σ, in contrast to the unique logarithmic decay in the long-time regime which does not depend on σ, ρ, n and the disorder, we find rich scaling structures including logarithmic and exponential-logarithmic scalings in the short-time regime. Non-universal critical scalings of Ising systems are also discussed for d=2σ.