We present results of large-scale Monte Carlo simulations for a three-dimensional Ising model with short-range interactions and planar defects, i.e., disorder perfectly correlated in two dimensions. We show that the phase transition in this system is smeared, i.e., there is no single critical temperature, but different parts of the system order at different temperatures. This is caused by effects similar to but stronger than Griffiths phenomena. In an infinite-size sample there is an exponentially small but finite probability to find an arbitrary large region devoid of impurities. Such a rare region can develop true long-range order while the bulk system is still in the disordered phase. We compute the thermodynamic magnetization and its finite-size effects, the local magnetization, and the probability distribution of the ordering temperatures for different samples. Our Monte-Carlo results are in good agreement with a recent theory based on extremal statistics.
R. Sknepnek and T. Vojta, "Smeared Phase Transition in a Three-Dimensional Ising Model with Planar Defects: Monte Carlo Simulations," Physical Review B: Condensed Matter and Materials Physics, American Physical Society (APS), Jan 2004.
The definitive version is available at https://doi.org/10.1103/PhysRevB.69.174410
University of Missouri Research Board
Keywords and Phrases
Ising model; Monte Carlo method; Phase transformations (Statistical physics)
Article - Journal
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