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'''Lattice hard spheres''' | '''Lattice hard spheres''' refers to athermal [[lattice gas|lattice gas]] models, in which pairs | ||
of sites separated by less than some short distance <math> \sigma </math> cannot be simultaneously occupied. | |||
== Brief description of the models == | == Brief description of the models == | ||
Basically the differences | Basically the differences with the standard [[Lattice gas|lattice gas]] model ([[Ising Models|Ising model]]) are: | ||
*An occupied site excludes the occupation of some of the | |||
*No energy interactions between pairs of occupied sites | *An occupied site excludes the occupation of some of the neighboring sites. | ||
These systems exhibit phase (order-disorder) transitions | |||
*No energy interactions between pairs of occupied sites are considered. | |||
These systems exhibit phase (order-disorder) transitions | |||
== Three-dimensional lattices == | == Three-dimensional lattices == | ||
*See Ref. 1 for some results of three-dimensional lattice hard sphere systems (on a [[Building up a simple cubic lattice |simple cubic lattice]]) | |||
If next-nearest neighbours are | The model defined on a simple cubic lattice with exclusion of ony the nearest neighbour positions of an occupied site, presents | ||
a continuous transition | |||
If also next-nearest neighbours are excluded, then the transition becomes first order (See Ref 1). | |||
== Two-dimensional lattices == | == Two-dimensional lattices == | ||
=== Square lattice === | === Square lattice === | ||
*See Ref 2. for results of two-dimensional systems (lattice hard disks) on a [[building up a square lattice|square lattice]]. | |||
on a [[building up a square lattice|square lattice]] | |||
=== [[Building up a triangular lattice|Triangular lattice]] === | === [[Building up a triangular lattice|Triangular lattice]] === | ||
The [[hard hexagon lattice model|hard hexagon lattice model]] belongs to this kind of | The [[hard hexagon lattice model|hard hexagon lattice model]] belongs to this kind of models. In this model an occupied site | ||
Other models defined on the triangular lattice (with more excluded positions) have been studied theoretically and by [[Monte Carlo | Monte Carlo simulation]] | excluded the occupation of nearest neighbour positions. This model exhibits a continous transition. (See references | ||
in the entry: [[hard hexagon lattice model|hard hexagon lattice model]]). | |||
Other models defined on the triangular lattice (with more excluded positions) have been studied theoretically and by [[Monte Carlo | Monte Carlo simulation]] (Refs 3-4). | |||
It seems that the model | It seems (see Ref. 3) that the model that includes first and second neighbour exclusion presents also a continuous transition, whereas if third neigbours are also excluded the | ||
transition becomes first order. | |||
== References == | == References == | ||
#[http://dx.doi.org/10.1063/1.2008253 A. Z. Panagiotopoulos, "Thermodynamic properties of lattice hard-sphere models", J. Chem. Phys. 123, 104504 (2005) ] | |||
#[http://dx.doi.org/10.1063/1.2539141 Heitor C. Marques Fernandes, Jeferson J. Arenzon, and Yan Levin "Monte Carlo simulations of two-dimensional hard core lattice gases" J. Chem. Phys. 126, 114508 (2007).] | |||
#[http://dx.doi.org/10.1103/PhysRevB.30.5339 N. C. Bartelt and T. L. Einstein, "Triangular lattice gas with first- and second-neighbor exclusions: Continuous transition in the four-state Potts universality class" Phys. Rev. B 30, 5339 - 5341 (1984).] | |||
#[http://dx.doi.org/10.1103/PhysRevB.39.2948 Chin-Kun Hu and Kit-Sing Mak, "Percolation and phase transitions of hard-core particles on lattices: Monte Carlo approach", Phys. Rev. B 39, 2948 - 2951 (1989).] | |||
[[category: models]] | [[category: models]] | ||