TY - JOUR

T1 - Exact partition functions of the Ising model on M × N planar lattices with periodic-aperiodic boundary conditions

AU - Wu, Ming Chya

AU - Hu, Chin Kun

PY - 2002/6/28

Y1 - 2002/6/28

N2 - The Grassmann path integral approach is used to calculate exact partition functions of the Ising model on M × N square (sq), plane triangular (pt) and honeycomb (he) 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/kB, as a function of temperature, θ = kBT/J. We find that for the N × N sq lattice, C/kB for pa and ap boundary conditions are different from those for aa boundary conditions, but for the N × W pt and he lattices, C/kB 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.

AB - The Grassmann path integral approach is used to calculate exact partition functions of the Ising model on M × N square (sq), plane triangular (pt) and honeycomb (he) 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/kB, as a function of temperature, θ = kBT/J. We find that for the N × N sq lattice, C/kB for pa and ap boundary conditions are different from those for aa boundary conditions, but for the N × W pt and he lattices, C/kB 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.

UR - http://www.scopus.com/inward/record.url?scp=0037189240&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/35/25/304

DO - 10.1088/0305-4470/35/25/304

M3 - 期刊論文

AN - SCOPUS:0037189240

SN - 0305-4470

VL - 35

SP - 5189

EP - 5206

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 25

ER -