Phase transition versus disorder: A criterion derived from a two-dimensional dynamic ferromagnetic model.
The dynamical equations for spin correlation functions for the two-dimensional Ising model are discussed for rapid-quench conditions. The temperature of the bath in which the Ising spins are immersed is postulated to be driven by the hyperbolic cooling program T(-1) = T(0) (-1) + bt (T(0) being the initial temperature, t the time, and b a constant). It is shown that for sufficiently large b the term in the dynamical equations that would normally drive the system into an ordered state would not have time to become effective so that the system freezes into a disordered state. The correlation length for the disordered state is characterized by the distance a random walker on a two-dimensional lattice would have been able to diffuse in the time required for the quench to reduce the temperature to some preassigned value.
Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742.
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