for the cumulants of the sigma field show universal behavior near the critical point, which are independent from some non-universal factors, such as the relaxation time or the evolution trajectory.

DOI: 10.22323/1.311.0026

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\tau_{\mbox{\tiny KZ}}

l_{\mbox{\tiny KZ}}

, and

\theta_{\mbox{\tiny KZ}}

, the constructed function

\bar{f}_n((\tau-\tau_c)/\tau_{\mbox{\tiny KZ}},\theta_{\mbox{\tiny KZ}})

for the cumulants of the sigma field show universal behavior near the critical point, which are independent from some non-universal factors, such as the relaxation time or the evolution trajectory.

N

problems and prove their universality with respect to protocol choice. We also introduce a protocol in which the critical point is approached asymptotically at late times with the system marginally out of equilibrium, wherein logarithmic violations to scaling and anomalous dimensions occur even in the simple Gaussian problem.

\mathbb{Z}_2

symmetry in the dynamic universality class of Model A in two spatial dimensions. The critical dynamics of the system is studied under a linear quench protocol, in which the external symmetry breaking field is changed at a constant rate through the critical point. We discuss the connection to the Kibble-Zurek mechanism and determine universal scaling functions, which fully describe the non-equilibrium evolution of the system near the critical point for all quench rates under consideration. We find that, while the scaling functions are non-trivial, the corresponding scaling exponents are fully determined by static critical exponents and the dynamic critical exponent.