Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2002-04-10
J. Phys. A 35, 5189-5206 (2002)
Physics
Condensed Matter
Statistical Mechanics
17 pages, 13 Postscript figures, uses iopams.sty, submitted to J. Phys. A: Math. Gen
Scientific paper
10.1088/0305-4470/35/25/304
The Grassmann path integral approach is used to calculate exact partition functions of the Ising model on MxN square (sq), plane triangular (pt) and honeycomb (hc) lattices with periodic-periodic (pp), periodic-antiperiodic (pa), antiperiodic-periodic (ap) and antiperiodic-antiperiodic (aa) boundary conditions. The partition functions are used to calculate and plot the specific heat, $C/k_B$, as a function of the temperature, $\theta =k_BT/J$. We find that for the NxN sq lattice, $C/k_B$ for pa and ap boundary conditions are different from those for aa boundary conditions, but for the NxN pt and hc lattices, $C/k_B$ for ap, pa, and aa boundary conditions have the same values. Our exact partition functions might also be useful for understanding the effects of lattice structures and boundary conditions on critical finite-size corrections of the Ising model.
Hu Chin-Kun
Wu Ming-Chya
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