Temperature scaling in Monte Carlo nonequilibrium relaxation

The nonequilibrium relaxation (NER) method is an alternative approach to overcome the critical slowing down in Monte Carlo simulations. In local-update algorithms, NER is based on the power-law critical relaxation derived from the dynamical finite-size scaling (DFSS) theory, and off-critical scaling behaviors are also derived from the same formalism. In cluster-update algorithms, critical nonequilibrium relaxation is described by the stretched-exponential formula [1-4], which can be derived phenomenologically [5]. In the present talk, we show that off-critical scaling behaviors in cluster-update algorithms can be formulated by generalizing the nonequilibrium-to-equilibrium scaling [1,3-5]. By taking the magnetic susceptibility as an example, from the early-time critical relaxation, χ(t)∼exp(ct^σ), and the equilibrium behavior near the critical point T_c, χ(T)∼(T-T_c)^-γ, we have χ(t,T)∼(T-T_c)^-γf_sc[ct^σ+log(T-T_c)^γ] with a scaling function f_sc(x). This scaling is confirmed numerically, and the one derived similarly in local-update algorithms holds better than that from DFSS.

[1] Y. Nonomura, J. Phys. Soc. Jpn. 83, 113001 (2014). [2] YN and Y. Tomita, PRE 92, 062121 (2015). [3] YN and YT, PRE 93, 012101 (2016). [4] YN and YT, arXiv:1907.06169. [5] YT and YN, PRE 98, 052110 (2018).