Two-temperature kinetic Ising model in one dimension: Steady-state correlations in terms of energy and energy flux

1994 ◽  
Vol 49 (1) ◽  
pp. 139-144 ◽  
Author(s):  
Z. Rácz ◽  
R. K. P. Zia
Keyword(s):  
Steady State ◽  
Ising Model ◽  
Energy Flux ◽  
One Dimension ◽  
Kinetic Ising Model ◽  
Two Temperature

An Analytical Approach to the Fredrickson–Andersen Model in One Dimension

1997 ◽  
Vol 11 (24) ◽  
pp. 2927-2940 ◽  
Author(s):  
Michael Schulz ◽  
Steffen Trimper
Keyword(s):  
Ising Model ◽  
Evolution Equations ◽  
Fock Space ◽  
One Dimension ◽  
Space Representation ◽  
Short Time Scale ◽  
Kinetic Ising Model ◽  
Andersen Model ◽  
Long Time ◽  
Short Time

The dynamics of a modified kinetic Ising model usual noted as Fredrickson–Andersen model (FAM) is formulated in terms of Pauli-operators using a Fock-space representation of the Master equation. The method is appropriate to study the cooperativity by including topological restrictions explicitly. Following the concept of the FAM the block distribution function of m+1 adjacent liquid-like (spin down) or solid-like (spin up) regions is analysed in one dimension. The hierarchy of evolution equations for those functions can be solved exactly at zero temperature leading to a double exponential decay and to a nonergodic behaviour. In case of nonzero temperatures, we are able to solve this set of infinite nonlinear first order differential equations only after a well motivated decoupling procedure. It results an implicit solution for the averaged density. For short time scale the system behaves like an ordinary Ising model with exponential relaxation. In the long time limit, we observe already in lowest order a crossover to an exponential screened algebraic decay with an universal exponent 3/2 and moreover, the relaxation time will be drastically enlarged.

scholarly journals Energy flux distribution in a two-temperature Ising model

2005 ◽  
Vol 2005 (02) ◽  
pp. P02008 ◽  
Author(s):  
Vivien Lecomte ◽  
Zoltán Rácz ◽  
Frédéric van Wijland
Keyword(s):  
Ising Model ◽  
Energy Flux ◽  
Flux Distribution ◽  
Two Temperature
Sign in / Sign up

Export Citation Format

Share Document