Parallel tempering and 3D spin glass models

We review parallel tempering schemes and examine their main ingredients for accuracy and efficiency. We discuss two selection methods of temperatures and some alternatives for the exchange of replicas, including all-pair exchange methods. We measure specific heat errors and round-trip efficiency using the two-dimensional (2D) Ising model, and also test the efficiency for the ground state production in 3D spin glass models. We find that the optimization of the GS problem is highly influenced by the choice of the temperature range of the PT process. Finally, we present numerical evidence concerning the universality aspects of an anisotropic case of the 3D spin-glass model.