Ising Model with Antiferromagnetic Next‐Nearest‐Neighbor Coupling. III. Disorder Points, Energy Points, and Scattering from a One‐Dimensional Model

1971 ◽  
Vol 42 (4) ◽  
pp. 1278-1279 ◽  
Author(s):  
John Stephenson
Keyword(s):  
Ising Model ◽  
Nearest Neighbor ◽  
Dimensional Model ◽  
One Dimensional ◽  
Nearest Neighbor Coupling

scholarly journals EXACT SOLUTION OF AN IRREVERSIBLE ONE-DIMENSIONAL MODEL WITH FULLY BIASED SPIN EXCHANGES

1996 ◽  
Vol 10 (25) ◽  
pp. 3451-3459 ◽  
Author(s):  
ANTÓNIO M.R. CADILHE ◽  
VLADIMIR PRIVMAN
Keyword(s):  
Exact Solution ◽  
Domain Wall ◽  
Nearest Neighbor ◽  
Spin Exchange ◽  
Initial Conditions ◽  
Strong Dependence ◽  
Zero Temperature ◽  
Dimensional Model ◽  
One Dimensional ◽  
Temperature Dynamics

We introduce a model with conserved dynamics, where nearest neighbor pairs of spins ↑↓ (↓↑) can exchange to assume the configuration ↓↑ (↑↓), with rate β(α), through energy decreasing moves only. We report exact solution for the case when one of the rates, α or β, is zero. The irreversibility of such zero-temperature dynamics results in strong dependence on the initial conditions. Domain wall arguments suggest that for more general, finite-temperature models with steady states the dynamical critical exponent for the anisotropic spin exchange is different from the isotropic value.

Thermal conduction in a quasi-stationary one-dimensional lattice system

2019 ◽  
Vol 33 (17) ◽  
pp. 1950178
Author(s):  
Mohammad Khorrami ◽  
Amir Aghamohammadi
Keyword(s):  
Heat Transfer ◽  
Ising Model ◽  
Diffusion Equation ◽  
Thermal Conduction ◽  
Nearest Neighbor ◽  
Entropy Change ◽  
Neighbor Interaction ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Special Case

A system of nearest-neighbor interaction on a one-dimensional lattice is investigated, which has a quasi-stationary (and position-dependent) temperature profile. The rates of heat transfer and entropy change, as well as the diffusion equation for the temperature are studied. A q-state Potts model, and its special case, a two-state Ising model, are considered as an example.

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