Crossover from anomalous to normal diffusion: Ising model with stochastic resetting

In this paper, we investigate the dynamics of the two-dimensional Ising model with stochastic resetting, utilizing a constant resetting rate procedure with zero-strength initial magnetization. Our results reveal the presence of a characteristic rate <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:msub><a:mi>r</a:mi><a:mi>c</a:mi></a:msub><a:mo>∼</a:mo><a:msup><a:mi>L</a:mi><a:mrow><a:mo>−</a:mo><a:mi>z</a:mi></a:mrow></a:msup></a:mrow></a:math>, where <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>L</b:mi></b:math> represents the system size and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>z</c:mi></c:math> denotes the dynamical exponent. Below <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:msub><d:mi>r</d:mi><d:mi>c</d:mi></d:msub></d:math>, both the equilibrium and dynamical properties remain unchanged. At the same time, for <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mi>r</e:mi><e:mo>&gt;</e:mo><e:msub><e:mi>r</e:mi><e:mi>c</e:mi></e:msub></e:mrow></e:math>, the resetting process induces a transition in the probability distribution of the magnetization from a double-peak distribution to a three-peak distribution, ultimately culminating in a single-peak exponential decay. Furthermore, we also find that at the critical points, as <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mi>r</f:mi></f:math> increases, the diffusion of the magnetization changes from anomalous to normal, and the correlation time shifts from being dependent on <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mi>L</g:mi></g:math> to being <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mi>r</h:mi></h:math>-dependent only. Published by the American Physical Society 2024