The grand canonical ABC model: a reflection asymmetric meanfield Potts model
Abstract
We investigate the phase diagram of a threecomponent system of particles on a onedimensional filled lattice, or equivalently of a onedimensional threestate Potts model, with reflection asymmetric meanfield interactions. The three types of particles are designated as A, B and C. The system is described by a grand canonical ensemble with temperature T and chemical potentials Tλ_{A}, Tλ_{B} and Tλ_{C}. We find that for λ_{A} = λ_{B} = λ_{C} the system undergoes a phase transition from a uniform density to a continuum of phases at a critical temperature \hat{T}_c=(2\pi /\sqrt{3})^{1}. For other values of the chemical potentials the system has a unique equilibrium state. As is the case for the canonical ensemble for this ABC model, the grand canonical ensemble is the stationary measure satisfying detailed balance for a natural dynamics. We note that \hat{T}_c=3T_c, where T_{c} is the critical temperature for a similar transition in the canonical ensemble at fixed equal densities r_{A} = r_{B} = r_{C} = 1/3.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 February 2011
 DOI:
 10.1088/17518113/44/6/065005
 arXiv:
 arXiv:1010.1180
 Bibcode:
 2011JPhA...44f5005B
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 24 pages, 3 figures