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We consider energy relaxation of the long-range spin glass model with sparsecouplings, the so-called dilute Sherrington-Kirkpatrick (SK) model, startingfrom a random initial state. We consider the effect that modularity of thecoupling matrix has on this relaxation dynamics. In the absence of finite sizeeffects, the relaxation dynamics appears independent of modularity. For finitesizes, a more modular system reaches a less favorable energy at long times. Forsmall sizes, a more modular system also has a less favorable energy at shorttimes. For large sizes, modularity appears to lead to slightly more favorableenergies at intermediate times. We discuss these results in the context ofevolutionary theory, where horizontal gene transfer, absent in the Glauberequilibration dynamics of the SK model studied here, endows modular organismswith larger response functions at short times.

On the Universality of the Energy Response Function in the Long-Range Spin Glass Model with Sparse, Modular Couplings