Condensed Matter > Statistical Mechanics
[Submitted on 1 Jul 2020 (v1), last revised 16 Nov 2020 (this version, v2)]
Title:Mapping distinct phase transitions to a neural network
View PDFAbstract:We demonstrate, by means of a convolutional neural network, that the features learned in the two-dimensional Ising model are sufficiently universal to predict the structure of symmetry-breaking phase transitions in considered systems irrespective of the universality class, order, and the presence of discrete or continuous degrees of freedom. No prior knowledge about the existence of a phase transition is required in the target system and its entire parameter space can be scanned with multiple histogram reweighting to discover one. We establish our approach in q-state Potts models and perform a calculation for the critical coupling and the critical exponents of the $\phi^{4}$ scalar field theory using quantities derived from the neural network implementation. We view the machine learning algorithm as a mapping that associates each configuration across different systems to its corresponding phase and elaborate on implications for the discovery of unknown phase transitions.
Submission history
From: Dimitrios Bachtis [view email][v1] Wed, 1 Jul 2020 09:46:05 UTC (713 KB)
[v2] Mon, 16 Nov 2020 16:08:14 UTC (708 KB)
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