The phase transition in the simple cubic ising lattice

Chengxiang Ding, Wenan Guo, Youjin Deng

By means of Monte Carlo simulations and a finite-size scaling analysis, we find a critical line of an n-component Eulerian face-cubic model on the square lattice and the simple cubic lattice in the region v>1, where v is the bond weight. The phase transition belongs to the Ising universality class independent of n. The critical properties of the phase transition can also be captured by the percolation of the complement of the Eulerian graph.

Valeriy A Ryabov

R. E. Hetzel, R. N. Bhatt, Rajiv R. P. Singh

We explore the behavior of the nearest-neighbor Ising spin glass with discrete bonds (± J ) on the face-centered cubic lattice using both Monte Carlo simulations and high-temperature expansions. A phase transition to a spin glass phase is found in zero magnetic field ( H ) at a nonzero temperature ( T = T c ), with critical exponents close to that for the simple cubic lattice. In the ( H, T )-plane, the contours of constant spin glass susceptibility show an upturn towards higher H at the lowest T , consistent with the possibility of a de Almeida-Thouless line of phase transitions in a field. Further, the upturn is similar to those on the simple cubic lattice and less pronounced than on the four-dimensional hypercubic lattice, despite the higher coordination number of the f.c.c. lattice, suggesting that the upturn is a dimension-related property.

H Ulman, M Athematics J Ournal

Arnold M. Kosevich, V. A. Shklovskiǐ

H. Mohammadi Kamrava, M. Barati

Within the effective-field theory with correlations (EFT), a transverse random field spin-1 Ising model on the simple cubic (z=6) lattice is studied. The phase diagrams, the behavior of critical points, transverse magnetization,  internal energy, magnetic specific heat are obtained numerically and discussed for different values of p the concentration of the random transverse field.