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New Physics Sae Mulli

Nonequilibrium critical dynamics of two dimensional Ising model under slow cooling and heating

Kangeun Jeong, Bongsoo Kim, Sung Jong Lee

Published Feb 26, 2021• 2 citations
Publisher
DOI
10.3938/npsm.71.200

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We discuss the limit cycle regime of a finite-time quantum Otto cycle with a frictionless two-dimensional anisotropic Ising model as the working fluid. From Onsager's exact equilibrium solution, we first find optimal parameters for the operational modes of work extraction and cooling for infinitely slow cycles. The equilibrium points in these optimal cycles correspond to different phases of the model, such that the nonequilibrium dynamics during the cycle bypasses the phase transition. Finite-time cycles allow for finite power extraction or cooling currents, but for such cycles, we point out that-already within the regime of weak system-reservoir coupling-energetic changes of the system during dissipative strokes may contain a significant portion of coupling and decoupling control work and should thus not be directly identified with heat. For ultrafast cycles, the required control work spoils performance, such that to maximize work extraction or cooling heat per cycle time, there is an optimal cycle duration. We also find that net-zero-energy transitions may lead to undesired reservoir heating.
The coherent-anomaly method (CAM) is applied to the kinetic Ising model. Dynamical cluster-mean-field approximations are formulated to obtain a series of the dynamical mean-field critical coefficients. The coherent-anomaly scaling relations are derived on the basis of the scaling form of the generating function in nonequilibrium systems to estimate the exponent Δ of the critical slowing down. The dynamical critical exponent is estimated as Δ⋍2.15(±0.02){\varDelta}{\backsimeq}2.15({\pm}0.02)Δ⋍2.15(±0.02) for the kinetic Ising model on the two-dimensional triangular lattice.
As a simplified description of the nonequilibrium dynamics of buckled dimers on the Si(001) surface, we consider the anisotropic two-dimensional (2D) Ising model and study the freezing of spatial correlations during a cooling quench across the critical point. Depending on the cooling rate, we observe a crossover from one-dimensional (1D) to 2D behavior. For rapid cooling, we find effectively 1D behavior in the strongly coupled direction, for which we provide an exact analytic solution of the nonequilibrium dynamics. For slower cooling rates, we start to see 2D behavior where our numerical simulations show an approach to the usual Kibble-Zurek scaling in 2D.