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The following image is taken from an article and shows the hamiltonian of a spin chain model. I knew that the dimensional units in an equation must balance. To ensure this, the author took a procedure (as shown in the shaded part). With this procedure, he concluded that all parameters, J1, J2, and \lambda, have no units and hence the equation is balanced. I cannot understand this step and what is the final unit of the equation?

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All three coefficinets have dimensions of energy, so $J_2/J_1$ and $\lambda/J_1$ are dimensionless.

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  • $\begingroup$ But what he means by abs[J1]=1? and he said that all parameters are dimensionless, not the rations J2/J1 and λ/J1. @mike_atone $\endgroup$
    – Bekaso
    Feb 14, 2020 at 17:38
  • $\begingroup$ He just takes $J_1=1$ in whatever units he feels like. None of it affects anything. The phases of the spn chain are determined only by the ratios of the couplings. Nobody cares about the overall-energy scale in these type of models. $\endgroup$
    – mike stone
    Feb 14, 2020 at 17:43
  • $\begingroup$ By "scaled to $J_1$" he means divided by $J_1$. $\endgroup$
    – mike stone
    Feb 14, 2020 at 18:10

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