Ising models on the hydrogen peroxide and other lattices

Abstract

We perform a Monte Carlo analysis of the Ising model on many three-dimensional lattices. By means of finite-size scaling we obtain the critical points and determine the scaling dimensions. As expected, the critical exponents agree with the three-dimensional Ising universality class for all models. The irrelevant field, as revealed by the correction-to-scaling amplitudes, appears to be relatively large. Combining the Monte Carlo results for the hydrogen peroxide lattice with those for five other three-dimensional lattices, we obtain a set of data covering a wide range of the irrelevant temperature field. This is helpful in the determination of the parameters describing the corrections to scaling. As a consequence, new results are obtained for the universal parameters describing Ising criticality in three dimensions, with reduced error margins in comparison with earlier Monte Carlo analyses. The critical exponents describing the thermodynamic singularities are determined by the temperature renormalization exponent $y_t = 1.58693 (9)$ and the magnetic renormalization exponent $y_h = 2.48178 (5)$. The corrections to scaling are governed by the irrelevant exponent $y_1 = -0.821 (5)$.

Figures (2)

• Figure 1: Sketch of the hydrogen peroxide lattice. The Ising spins are located at the vertices of the lattice. Each spin interacts with three nearest neighbors. The nearest-neighbor couplings are shown as solid lines. The hydrogen peroxide lattice has cubic symmetry, and all sites are equivalent. In this sketch, the lattice sites coincide with those of the simple cubic lattice, but the number of spin-spin couplings is less by a factor of two.
• Figure 2: Sketch of positions of models 1-6 in the parameter space $(r, v)$ of the $\phi^4$ model, where $r$ is a temperature-like parameter, and the $\phi^4$ amplitude $v$ parametrizes the irrelevant field of the Ising model. The positions of the six models are shown by black circles ( $\bullet$ ). The mean-field and Ising fixed points, which are shown as open circles ( $\circ$ ), are located at $(-r, v){=}(0, 0)$ and $(-r^*, v^*)$, respectively.