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School of Physics Colloquium Series: Presenting Sidney Redner, Boston University
What could possibly be new in the Ising model, arguably the most-studied model of statistical physics? Plenty! Consider the Ising model initially at infinite temperature that is suddenly cooled to zero temperature and evolves by single spin-flip dynamics. What happens? In one dimension, the ground state is always reached and the evolution can be solved exactly. In two dimensions, the ground state is reached only about 2/3 of the time, and the long-time evolution is characterized by two distinct time scales, the longer of which arises from topological defects. In three dimensions, the ground state is never reached and the evolution is quite rich: (i) domains are topologically complex, with average genus growing algebraically with system size; (ii) the long-time state always contains "blinker" spins that can flip ad infinitum with no energy cost; (iii) the relaxation time grows
exponentially with system size.