The grand canonical ABC model: a reflection asymmetric mean field Potts model
| Autor: | Barton, John, Lebowitz, Joel L., Speer, Eugene R. |
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| Rok vydání: | 2010 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1751-8113/44/6/065005 |
| Popis: | We investigate the phase diagram of a three-component system of particles on a one-dimensional filled lattice, or equivalently of a one-dimensional three-state Potts model, with reflection asymmetric mean field 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 $T\lambda_A$, $T\lambda_B$, and $T\lambda_C$. We find that for $\lambda_A=\lambda_B=\lambda_C$ the system undergoes a phase transition from a uniform density to a continuum of phases at a critical temperature $\hat T_c=(2\pi/\sqrt3)^{-1}$. 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 $r_A=r_B=r_C=1/3$. Comment: 24 pages, 3 figures |
| Databáze: | arXiv |
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