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Vortex formation in two dimensions: When symmetry breaks, how big are the pieces?

Andrew Yates·Wojciech H. Zurek
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Abstract

We investigate the dynamics of second order phase transitions in two dimensions, breaking a gauged U(1) symmetry. Using numerical simulations, we show that the density of topological defects formed scales with the quench timescale $τ_Q$ as $n \sim τ_Q^{-1/2}$ when the dynamics is overdamped at the instant when the freezeout of thermal fluctuations takes place, and $n \sim τ_Q^{-2/3}$ in the underdamped case. This is predicted by the scenario proposed by one of us [1].

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Andrew Yates, Wojciech H. Zurek. 1998-01-06. Vortex formation in two dimensions: When symmetry breaks, how big are the pieces?. https://doi.org/10.1103/physrevlett.80.5477

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