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2

I'm not a 100% this will address the question, so this might be more of a long comment than an answer. My main point is, perhaps, that given a Hamiltonian, you'll still want to specify the dynamics to do simulations. Even the Ising model can be simulated in several different ways, all satisfying detailed balance, where the relaxation towards equilibrium is ...

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Suppose the spins on the sites of the square lattice are coupled nearest neighbor so that the Hamiltonian is defined as $$H=-J\sum_{<ij>}S_iS_j$$ where $<ij>$ denotes nearest neighbors $i$ and $j$ (each site has 4 nearest neighbors). The ground state of the Hamiltonian will be given by finding a configuration of spins $\{S_i\}$ for which the ...

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The state with minimal energy will be an alteration of +1 and -1 spins. The reason is that the 1-4 interactions will dominate the rest. Each spin in your system will interact with 6 others. Even though 1-2 (neighbours) and 1-3 interactions will be unfavourable in the alternating sequence, two favourable 1-4 interactions with the weight -4 will have more ...

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