Crossover from a Fractal Lattice to an Euclidean Lattice for the
Thermodynamic Properties of a Four-Spin Interaction Ising Model
LI Jianhua, QIN Yong*
Department of Physics, Education College of Ningxia and Teacher Academy of Yinchuan, Yinchuan 750002
*CCAST (World Laboratory) P. O. Box 8730, Beijing 100080
Department of Physics, Beijing Normal University, Beijing 100875
Crossover from a Fractal Lattice to an Euclidean Lattice for the
Thermodynamic Properties of a Four-Spin Interaction Ising Model
LI Jianhua;QIN Yong*
Department of Physics, Education College of Ningxia and Teacher Academy of Yinchuan, Yinchuan 750002
*CCAST (World Laboratory) P. O. Box 8730, Beijing 100080
Department of Physics, Beijing Normal University, Beijing 100875
Abstract： We study how thermodynamic properties of the four-spin interaction Ising model on a family of Sierpinski carpets fractals cross over to that of the Ising model on square lattice with four-spin interaction in half of the square faces. The exact free energy fs for the square model and ff for the fractals are obtained in a closed form and found to be analytic in temperature. The free energy varies smoothly with the geometrical parameter b (which labels each member of the fractal family) and for large b the difference between fs and ff is asymptotically proportional to l/b2.
LI Jianhua;QIN Yong*. Crossover from a Fractal Lattice to an Euclidean Lattice for the
Thermodynamic Properties of a Four-Spin Interaction Ising Model[J]. 中国物理快报, 1995, 12(6): 370-373.
LI Jianhua, QIN Yong*. Crossover from a Fractal Lattice to an Euclidean Lattice for the
Thermodynamic Properties of a Four-Spin Interaction Ising Model. Chin. Phys. Lett., 1995, 12(6): 370-373.
1995, Vol. 12 
