scholarly journals Correlation Functions of a One-Dimensional Lattice Gas with Nearest-Neighbor and Next-Nearest-Neighbor Interactions

1987 ◽  
Vol 77 (1) ◽  
pp. 68-83 ◽  
Author(s):  
K. Tanaka ◽  
T. Morita ◽  
K. Hiroike
Keyword(s):  
Correlation Functions ◽  
Lattice Gas ◽  
Nearest Neighbor ◽  
Dimensional Lattice ◽  
One Dimensional

Statistical Thermodynamics and Surface Phase Transitions of Interacting Particles Adsorbed on One-Dimensional Channels Arranged in a Triangular Cross-Sectional Structure

2009 ◽  
Vol 150 ◽  
pp. 73-100 ◽  
Author(s):  
P.M. Pasinetti ◽  
F. Romá ◽  
J.L. Riccardo ◽  
A.J. Ramirez-Pastor
Keyword(s):  
Monte Carlo ◽  
Interaction Energy ◽  
Lattice Gas ◽  
Nearest Neighbor ◽  
Single Channel ◽  
Scaling Analysis ◽  
Surface Phase ◽  
Cross Sectional ◽  
One Dimensional ◽  
Sectional Structure

Monte Carlo simulations and finite-size scaling analysis have been carried out to study the critical behavior in a submonolayer lattice-gas, which mimics a nanoporous environment. In this model, one-dimensional chains of atoms were arranged in a triangular cross-sectional structure. Two kinds of lateral interaction energies have been considered: (1) wL, interaction energy between nearest-neighbor particles adsorbed along a single channel and (2) wT, interaction energy between particles adsorbed across nearest-neighbor channels. We focus on the case of repulsive transverse interactions (wT > 0), where a rich variety of structural orderings are observed in the adlayer, depending on the value of the parameters kBT/wT (kB being the Boltzmann constant) and wL /wT. For wL /wT = 0, successive planes are uncorrelated, the system is equivalent to the triangular lattice, and the well-known [ ] ordered phase is found at low temperatures and a coverage, , of 1/3 [2/3]. In the more general case (wL /wT  0), the competition between interactions along a single channel and the transverse coupling between sites in neighboring channels leads to a three-dimensional adsorbed layer. Consequently, the and structures “propagate” along the channels and new ordered phases appear in the adlayer. The influence of each ordered phase on adsorption isotherms, differential heat of adsorption and configurational entropy of the adlayer has been analyzed and discussed in the context of the lattice-gas theory. Finally, the Monte Carlo technique was combined with the recently reported free energy minimization criterion approach (FEMCA) [F. Romá et al.: Phys. Rev. B Vol. 68 (2003), art. no. 205407] to predict the critical temperatures of the surface-phase transformations occurring in the adsorbate. The excellent qualitative agreement between simulated data and FEMCA results allows us to interpret the physical meaning of the mechanisms underlying the observed transitions.

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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