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We have investigated the phase transition in the Heisenberg spin glass using massive numerical simulations to study larger sizes, 48x48x48, than have been attempted before at a spin glass phase transition.
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To our knowledge, a 48 3 48^{3} lattice is the largest spin glass that has been thermalized near a finite temperature phase transition. It is curious that larger sizes can be studied for the Heisenberg model than for the Ising cases (for which the 28 3 28^{3} samples studied by Hasenbusch et al. [ 3 ] seems to be the record), even though the updating code is more complicated. Evidently, the barriers between “valleys” are lower in the Heisenberg model
Cited in the paper.
For the CG, one considers a transverse or parallel ξ C G , L \xi_{CG,L} , depending on whether μ ^ ⋅ 𝒌 min = 0 \hat{\mu}\cdot\bm{k}_{\text{min}}=0 or not [ 7 , 8 ] . We report only the parallel ξ CG , L \xi_{\text{CG},L} as the two coincide within errors
Cited in the paper.
Given the set of temperatures { T i } \{T_{i}\} , let f ( T ) f(T) be a cubic polynomial in T − 1 T^{-1} (unique up to an irrelevant multiplicative constant) with ∑ i f ( T i ) = 0 \sum_{i}f(T_{i})\!=\!0 , f ′ ( T max ) = 0 f^{\prime}(T_{\text{max}})=0 and changing sign at 0.14 ≈ T c 0.14\approx T_{\text{c}} . Let f t f_{t} be f ( T ) f(T) for the T T occupied by one copy of the system at time t t . We first coarse grain f t f_{t} by averaging over 100 consecutive MC sweeps, then compute its autocorrelation function and integrated autocorrelation time (see e.g. Refs. 26 , 15 )
Cited in the paper.