Two-dimensional Ising criticality in interacting electron systems

Hiromi Otsuka, Masaaki Nakamura

Kazuhiko Minami, Masuo Suzuki

Helmut G. Katzgraber, L. W. Lee, Ian A. Campbell

Monte Carlo data of the two-dimensional Ising spin glass with bimodal interactions are presented with the aim of understanding the low-temperature physics of the model. An analysis of the specific heat, spin-glass susceptibility, finite-size correlation length, and the Binder ratio is performed to try to verify a recent proposal in which for large system sizes and finite but low temperatures the effective critical exponents are identical to the critical exponents of the two-dimensional Ising spin glass with Gaussian interactions. Our results show that with present system sizes the recently proposed scenario, in which the two-dimensional Ising spin glass with bimodally distributed interactions is in the same universality class as the model with Gaussian-distributed disorder at low but finite temperatures, cannot be reliably proven.

Young C. Kim, Mikhail A. Anisimov, Jan V. Sengers +1 more

Seizo Watarai, Keizô Yamamoto, Akira Nakanishi

Monte Carlo simulations are performed on the square lattice Ising system with both the nearest neighbor and the two-dimensional dipolar interactions in order to investigate the critical property of ferromagnetic phase transitions in this 2-dimensional system. Applying the finite size scaling theory to Monte Carlo data just near the transition point, the critical indices of this dipolar system are calculated and α=0.31±0.04, β =0.20±0.02, γ=1.08±0.20 and ν=0.72±0.10 are obtained. However, in the temperature region considerably far from the transition point, different values of α, β and γ seem to be adequate, which are rather close to those of the rigorous result of the 2-dimensional Ising model.

Hans-Otto Heuer