Crossover from a Fractal Lattice to an Euclidean Lattice for the Thermodynamic Properties of a Four-Spin Interaction Ising Model

摘要

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 f_(s) for the square model and f_(j) 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 f_(s) and f_(j) is asymptotically proportional to 1/b^(2).