SHORT-TIME DYNAMICS OF THE RANDOM n-VECTOR MODEL WITH LONG-RANGE INTERACTION

2003 ◽  
Vol 17 (23) ◽  
pp. 1227-1236 ◽  
Author(s):  
YUAN CHEN ◽  
ZHI-BING LI
Keyword(s):  
Long Range ◽  
High Temperature Phase ◽  
Vector Model ◽  
Temperature Phase ◽  
Range Interaction ◽  
Time Dynamics ◽  
Long Range Interaction ◽  
Renormalization Group Approach ◽  
Short Time ◽  
N Vector

The short-time critical behavior of the random n-vector model with long-range interaction is studied by the theoretic renormalization-group approach. After a sudden quench to the critical temperature from the high temperature phase, the system is released to an evolution within model A dynamics. The initial slip exponents and the dynamic exponent are calculated to two-loop order.

THE AGING BEHAVIOR OF THE RANDOM n-VECTOR MODEL WITH LONG-RANGE INTERACTION

2007 ◽  
Vol 21 (23) ◽  
pp. 1555-1568 ◽  
Author(s):  
YUAN CHEN
Keyword(s):  
Long Range ◽  
Vector Model ◽  
Aging Behavior ◽  
Range Interaction ◽  
Fluctuation Dissipation ◽  
Long Range Interaction ◽  
Renormalization Group Approach ◽  
Long Time ◽  
Short Time ◽  
N Vector

The aging behavior of the random n-vector model with long-range interaction decaying as r-(d+σ) (where d is the dimensionality), is investigated by the theoretic renormalization-group approach. The system initially disordered at a high temperature is firstly quenched to the critical temperature T c and then released to an evolution with model A dynamics. The aging properties are studied by the short-time expansions. The scaling behavior of two-time response and correlation functions are obtained in a frame of the expansion in ∊ = 2σ-d. In dimensions d < 2σ, the long-time limit of the critical fluctuation dissipation ratio X∞ is calculated up to one-loop order. The simulation of X∞ is discussed.

scholarly journals The short-time critical behaviour of the Ginzburg-Landau model with long-range interaction

2000 ◽  
Vol 18 (2) ◽  
pp. 289-296 ◽  
Author(s):  
Y. Chen ◽  
S.H. Guo ◽  
Z.B. Li ◽  
S. Marculescu ◽  
L. Schülke
Keyword(s):  
Long Range ◽  
Critical Behaviour ◽  
Range Interaction ◽  
Ginzburg Landau ◽  
Landau Model ◽  
Long Range Interaction ◽  
Time Critical ◽  
Short Time

scholarly journals Long-range vector models at large N

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Noam Chai ◽  
Mikhail Goykhman ◽  
Ritam Sinha
Keyword(s):  
Long Range ◽  
Short Range ◽  
Conformal Symmetry ◽  
Vector Model ◽  
Entire Region ◽  
Crossover Point ◽  
Range Interaction ◽  
Large N ◽  
Long Range Interaction ◽  
Range Vector

Abstract We calculate various CFT data for the O(N) vector model with the long-range interaction, working at the next-to-leading order in the 1/N expansion. Our results provide additional evidence for the existence of conformal symmetry at the long-range fixed point, as well as the continuity of the CFT data at the long-range to short-range crossover point s* of the exponent parameter s. We also develop the N > 1 generalization of the recently proposed IR duality between the long-range and the deformed short-range models, providing further evidence for its non-perturbative validity in the entire region d/2 < s < s*.

Short-Time Dynamics of the Random n -Vector Model

2001 ◽  
Vol 36 (5) ◽  
pp. 611-616
Author(s):  
Chen Yuan ◽  
Li Zhi-Bing ◽  
Fang Hai ◽  
He Shun-Shan ◽  
Situ Shu-Ping
Keyword(s):  
Vector Model ◽  
Time Dynamics ◽  
Short Time ◽  
N Vector

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

2001 ◽  
Vol 15 (02) ◽  
pp. 43-55 ◽  
Author(s):  
Z. B. LI ◽  
Y. CHEN ◽  
S. H. GUO
Keyword(s):  
Long Range ◽  
Scaling Laws ◽  
Quenched Disorder ◽  
Long Range Correlations ◽  
Time Dynamics ◽  
Time Regime ◽  
Renormalization Group Approach ◽  
Long Time ◽  
Logarithmic Decay ◽  
Short Time

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.

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