Almost all materials undergo spontaneous symmetry breaking at sufficiently low
temperatures. For most magnetic materials, the spin rotational symmetry is broken
to form magnetic ordering. The discovery of metallic alloys which fail to form
conventional magnetic order has remained a puzzle for the last few decades.
Unfortunately, analytical calculations cannot provide an unbiased answer for the
problem. Furthermore, on the numerical side, Monte Carlo simulations require
extremely long equilibration times. The parallel tempering method has proven a
powerful tool to alleviate the long equilibration time. With the extensive efforts of
numerical simulation research, some of the idealized models have been studied in
detail. The general consensus is that for models with uncorrelated disorder there
exists a finite spin glass critical temperature in three dimensions. However, it is not
hard to imagine that, in real materials, the disorder is somewhat correlated, meaning the correlation exists between a completely random distribution and the correlation you would see in a crystalline lattice. In this work, we employ modern spin glass simulation techniques to study a prototype spin glass model with correlated disorder. We find that the critical temperature is enhanced due to the correlated disorder.
Willard, Jared D.
"Simulating Correlated Disorder in Spin Glass,"
Macalester Journal of Physics and Astronomy: Vol. 3:
1, Article 9.
Available at: https://digitalcommons.macalester.edu/mjpa/vol3/iss1/9