Abstract
For the zero-temperature Glauber dynamics of theq-state Potts model, the fractionr(q, t) of spins which never flip up to timet decays like a power lawr(q, t)∼t −θ(q) when the initial condition is random. By mapping the problem onto an exactly soluble one-species coagulation model (A+A→A) or alternatively by transforming the problem into a free-fermion model, we obtain the exact expression of θ(q) for all values ofq. The exponent π(q) is in general irrational, θ(3)=0.53795082..., θ(4)=0.63151575..., ..., with the exception ofq=2 andq=∞, for which θ(2)=3/8 and θ(∞)=1.
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Derrida, B., Hakim, V. & Pasquier, V. Exact exponent for the number of persistent spins in the zero-temperature dynamics of the one-dimensional Potts model. J Stat Phys 85, 763–797 (1996). https://doi.org/10.1007/BF02199362
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DOI: https://doi.org/10.1007/BF02199362