In situations such as phase ordering or non-equilibrium critical dynamics, the two-time autoresponse function scales as $R(t,s)\\approx s^{-1-a} F_2(t/s)$ , where $a$ is a known exponent. For any value of the dynamical exponent $z$ , we argue that this dynamical scaling can be extended towards conformal invariance. Thus the scaling function $F_2$ is determined. This prediction is confirmed by several examples, both for $T<T_c$ and at $T=T_c$ : the two- and three-dimensional kinetic Ising model with Glauber dynamics is studied numerically, while exact results are available for the kinetic spherical model with a non-conserved order parameter, both for short-ranged and long-ranged interactions, as well as for the mean-field spherical spin glass.In situations such as phase ordering or non-equilibrium critical dynamics, the two-time autoresponse function scales as $R(t,s)\\approx s^{-1-a} F_2(t/s)$, where $a$ is a known exponent. For any value of the dynamical exponent $z$, we argue that this dynamical scaling can be extended towards conformal invariance. Thus the scaling function $F_2$ is determined. This prediction is confirmed by several examples, both for $T<T_c$ and at $T=T_c$: the two- and three-dimensional kinetic Ising model with Glauber dynamics is studied numerically, while exact results are available for the kinetic spherical model with a non-conserved order parameter, both for short-ranged and long-ranged interactions, as well as for the mean-field spherical spin glass.

arXiv:hep-th/0107122Jul 13, 20013 citations

Nonlinear critical dynamics of a spherical model

Zoltàn Ràcz, Tamás Tél

Physics Letters AJan 1, 197717 citations

Critical endpoints in the spherical model with rapidly decaying power-law interactions

Márcia C. Barbosa

Physica A Statistical Mechanics and its ApplicationsSep 1, 19918 citations

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

Yuan Chen

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.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.

Modern Physics Letters BOct 3, 20071 citation

Kinetics of the long-range spherical model

Florian Baumann, Sreedhar B Dutta, Malte Henkel

The kinetic spherical model with long-range interactions is studied after a quench to $T < T_c$ or to $T = T_c$ . For the two-time response and correlation functions of the order-parameter as well as for composite fields such as the energy density, the ageing exponents and the corresponding scaling functions are derived. The results are compared to the predictions which follow from local scale-invariance.The kinetic spherical model with long-range interactions is studied after a quench to $T < T_c$ or to $T = T_c$. For the two-time response and correlation functions of the order-parameter as well as for composite fields such as the energy density, the ageing exponents and the corresponding scaling functions are derived. The results are compared to the predictions which follow from local scale-invariance.

arXiv:cond-mat/0703445Journal of Physics A Mathematical and TheoreticalJun 19, 200722 citations

Finite-size shift of the critical temperature in the spherical model

Hassan Chamati, N. S. Tonchev

Journal of Statistical PhysicsJun 1, 19967 citations

In situations such as phase ordering or non-equilibrium critical dynamics, the two-time autoresponse function scales as

R(t,s)\\approx s^{-1-a} F_2(t/s)

, where

a

is a known exponent. For any value of the dynamical exponent

z

, we argue that this dynamical scaling can be extended towards conformal invariance. Thus the scaling function

F_2

is determined. This prediction is confirmed by several examples, both for

T<T_c

and at

T=T_c

: the two- and three-dimensional kinetic Ising model with Glauber dynamics is studied numerically, while exact results are available for the kinetic spherical model with a non-conserved order parameter, both for short-ranged and long-ranged interactions, as well as for the mean-field spherical spin glass.

The kinetic spherical model with long-range interactions is studied after a quench to

T < T_c

or to

T = T_c

. For the two-time response and correlation functions of the order-parameter as well as for composite fields such as the energy density, the ageing exponents and the corresponding scaling functions are derived. The results are compared to the predictions which follow from local scale-invariance.