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- W1518720525 abstract "Spin models are used in virtually every study of complex systems---be it condensed matter physics [1-4], neural networks [5] or economics [6,7]---as they exhibit very rich macroscopic behaviour despite their microscopic simplicity. It has long been known that by coarse-graining the system, the low energy physics of the models can be classified into different universality classes [8]. Here we establish a counterpart to this phenomenon: by fine-graining the system, we prove that all the physics of every classical spin model is exactly reproduced in the low energy sector of certain `universal models'. This means that (i) the low energy spectrum of the universal model is identical to the entire spectrum of the original model, (ii) the corresponding spin configurations are exactly reproduced, and (iii) the partition function is approximated to any desired precision. We prove necessary and sufficient conditions for a spin model to be universal, which show that complexity in the ground state alone is sufficient to reproduce full energy spectra. We use this to show that one of the simplest and most widely studied models, the 2D Ising model with fields, is universal." @default.
- W1518720525 created "2016-06-24" @default.
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- W1518720525 date "2014-06-23" @default.
- W1518720525 modified "2023-09-27" @default.
- W1518720525 title "Simple universal models capture all spin physics" @default.
- W1518720525 hasPublicationYear "2014" @default.
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