Existence of an ordered phase for the repulsive lattice gas on the FCC lattice
- 1 May 1980
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 13 (5) , 1803-1810
- https://doi.org/10.1088/0305-4470/13/5/039
Abstract
It is proven by Peierls' argument in connection with reflection positivity that the lattice gas on the FCC lattice with nearest-neighbour repulsion (with interaction energy a) exists in an ordered state at low enough temperature provided the chemical potential, mu , satisfies 0< mu <4a, 4a< mu <8a or 8a< mu <12a. This result immediately carries over to the antiferromagnetic Ising model and the lattice gas with nearest-neighbour exclusion on the FCC lattice, both of which will also exist in an ordered state under suitable circumstances. In particular, the existence of a phase transition at zero magnetic field is confirmed.Keywords
This publication has 10 references indexed in Scilit:
- Lattice models for liquid crystalsJournal of Statistical Physics, 1979
- Monte Carlo Study of an Ordering Alloy on an fcc LatticePhysical Review Letters, 1979
- The use of reflection as symmetry operation in connection with Peierls' argumentCommunications in Mathematical Physics, 1974
- One-nucleon transfer reactions on deformed nucleiPhysics Letters B, 1969
- The problem of uniqueness of a gibbsian random field and the problem of phase transitionsFunctional Analysis and Its Applications, 1969
- Analyticity properties of a lattice gasPhysics Letters A, 1967
- Existence of a Phase Transition in Two-Dimensional and Three-Dimensional Ising ModelsTheory of Probability and Its Applications, 1965
- Peierls Proof of Spontaneous Magnetization in a Two-Dimensional Ising FerromagnetPhysical Review B, 1964
- Ground State of an Ising Face-Centered Cubic LatticePhysical Review Letters, 1961
- Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising ModelPhysical Review B, 1952