Critical temperature in the two-layered Ising model

和彦 南

J. Wosiek

We have found a simple criterion which allows for the straightforward determination of the order-disorder critical temperatures. The method reproduces exactly known results for the two-dimensional Ising, Potts, and Z(N5) models. It also works for the Ising model on the triangular lattice. For systems that are not self-dual, our proposition remains an unproven conjecture. It predicts ${\mathrm{\ensuremath{\beta}}}_{\mathit{c}}$=0.2656. . . for the two coupled layers of Ising spins. The critical temperature of the three-dimensional Ising model is related to the free energy of the two-layer Ising system.

K. Herrmanns

Mehrdad Ghaemi, Mohammad Ghannadi, Behrouz Mirza

A new finite-size scaling approach based on the transfer matrix method is developed to calculate the critical temperature of an anisotropic two-layer Ising ferromagnet on strips of r -wide sites of square lattices. The reduced internal energy per site has been accurately calculated for the ferromagnetic case, with the nearest-neighbor couplings K x and K y (where K x and K y are the nearest-neighbor interactions within each layer in the x and y directions, respectively) and with interlayer coupling K z, using different size-limited lattices. The calculated energies for different lattice sizes intersect at various points when plotted versus the reduced temperature. It is found that the location of the intersection point versus the lattice size can be fitted to a power series in terms of the lattice sizes. The power series is used to obtain the critical temperature of the unlimited two-layer lattice. The results obtained are in good agreement with the accurate values reported by others.

Tomoyasu Tanaka

Zhibing Li, Zhigang Shuai, Q Wang +2 more

The symmetric two-layer Ising model (TLIM) is studied by the corner transfer matrix renormalization group method. The critical points and critical exponents are calculated. It is found that the TLIM belongs to the same universality class as the Ising model. The shift exponent is calculated to be 1.773, which is consistent with the theoretical prediction of 1.75 with 1.3% deviation.