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Spin systems with frustration and disorder are notoriously difficult to study both analytically and numerically.
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Jon Machta tells us that the method might also work for ferromagnetic systems at low temperatures. Here, the step of flipping the whole spin configuration of one replica if the two replicas are in opposite pure states is crucial. In this case both replicas will be in the same pure state (all spins up or all spins down), and the clusters will be small in a ferromagnet as well
Cited in the paper.
Note that in step (2a) of the ICM algorithm we flip the signs of the spins to reduce the overhead whenever the number of cluster sites exceeds N / 2 N/2 . To ensure that the measurement of observables is not affected by this operation, the signs of the flipped spins need to be kept track of
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Note that for the three-dimensional case, one may be tempted to think that clusters do not percolate because the spins are “frozen” below the critical temperature T c ∼ 1 T_{c}\sim 1 . However, this is not the case. In four space dimensions, T c ∼ 1.8 T_{c}\sim 1.8 [ 24 ] and p c = 0.197 p_{c}=0.197 [ 25 ] . However, clusters still only stop percolating for T ≲ 1 T\lesssim 1
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We note that our ICMs also slightly reduce autocorrelation times in addition to greatly improving thermalization times. However, note that the error due to configurational averages dominates in spin-glass simulations
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2014
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