Superdiffusion-like behavior in zero-temperature coarsening of the $$d=3$$ Ising model

Author:

Gessert Denis,Christiansen Henrik,Janke Wolfhard

Abstract

AbstractOne key aspect of coarsening following a quench below the critical temperature is domain growth. For the non-conserved Ising model a power-law growth of domains of like spins with exponent $$\alpha = 1/2$$ α = 1 / 2 is predicted. Including recent work, it was not possible to clearly observe this growth law in the special case of a zero-temperature quench in the three-dimensional model. Instead a slower growth with $$\alpha <1/2$$ α < 1 / 2 was reported. We attempt to clarify this discrepancy by running large-scale Monte Carlo simulations on simple-cubic lattices with linear lattice sizes up to $$L=2048$$ L = 2048 employing an efficient GPU implementation. Indeed, at late times we measure domain sizes compatible with the expected growth law—but surprisingly, at still later times domains even grow superdiffusively, i.e., with $$\alpha > 1/2$$ α > 1 / 2 . We argue that this new problem is possibly caused by sponge-like structures emerging at early times.

Funder

Deutsche Forschungsgemeinschaft

Engineering and Physical Sciences Research Council

Deutsch-Französische Hochschule

Universität Leipzig

Publisher

Springer Science and Business Media LLC

Subject

Multidisciplinary

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