Magnetisation Processes in Geometrically Frustrated Spin Networks with Self-Assembled Cliques

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. 2020 Mar 14;22(3):336. doi: 10.3390/e22030336

Algorithm A2 Program Flow: Field-driven spin dynamics on the graph

1:
INPUT: Graph $G$ , store as an array of Edge objects with identity of source and destination vertices, and the edges’s weight $w i j$ ; the defect edges are marked; the number of all edges is $N_{e}$ , the number of all vertices is N; input $Δ, c \leq 1$ ;
2:
Find $k_{m a x}$ the maximum number of nearest neighbours among vertices in $G$ ; set the external field to $h_{e x t} = - k_{m a x}$ ; reset time counter;
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Assign $J_{i j} = - 1$ to defect bonds, else $J_{i j} = + 1$ ;
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Attach two types of spins $s_{i}$ and $m_{i}$ (for parallel update) to each vertex; initialise the spin state as:
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for all vertices $i \in G$ do
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set $s_{i} = - 1$ and $m_{i} = - 1$ ; the magnetisation $M = \sum_{i} m_{i} = - N$ ;
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end for
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while $h_{e x t} < + k_{m a x}$ do
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Field ramping $h_{e x t} = h_{e x t} + Δ$ to trigger spin flips; Reset avalanche counters;
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Flips: reset counter of flipped spins $n_{f l i p}$ ;
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for all vertices $i \in G$ do
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compute local field $h_{i}^{l o c}$ as the sum $J_{i j} s_{j}$ over all nearest neighbours and add the current $h_{e x t}$ ;
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check the orientation of the spin $s_{i}$ and the local field and, and with prob. c, flip the spin to align it with the local filed; for parallel update, the auxiliary spin $m_{i}$ is flipped;
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count the number of flipped spins $n_{f l i p}$ ; update M from the number of flipped $m_{i}$ spins;
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end for
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update time t; sample temporal variables;
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Swap spins $s_{i} = m_{i}$ at all vertices;
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if $n_{f l i p} > 0$ then
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go to Flips and repeat the process;
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else
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Determine the avalanche size from the number of flipped spins;
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end if
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end while
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Sample the data of interest;
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END