A learning by confusion approach to characterize phase transitions

TL;DR

This paper investigates the applicability of the learning by confusion (LBC) method to identify and characterize both continuous and discontinuous phase transitions in various microscopic models, revealing its limitations and potential.

Contribution

It extends the LBC approach to discontinuous phase transitions and analyzes factors affecting its effectiveness across different models.

Findings

LBC can sometimes distinguish phase transition order.

Phase coexistence can increase neural network confusion.

Effectiveness of LBC varies with transition type and model parameters.

Abstract

Recently, the learning by confusion (LBC) approach has been proposed as a machine learning tool to determine the critical temperature Tc of phase transitions without any prior knowledge of its even approximate value. However, the effectiveness of the method has been demonstrated only for continuous phase transitions, where confusion can result only from a deliberate incorrect labeling of the data and not from the coexistence of different phases. To verify whether the confusion scheme can also be used for discontinuous phase transitions, in this work, we apply the LBC method to three microscopic models, the Blume-Capel, the q-state Potts, and the Falicov-Kimball models, which undergo continuous or discontinuous phase transitions depending on model parameters. With the help of a simple model, we predict that the phase coexistence present in discontinuous phase transitions can make the neural network more confused and thus decrease its performance. However, numerical calculations performed for the models mentioned above indicate that other aspects of this kind of phase transition are more important and can render the LBC method less effective. Nevertheless, we demonstrate that in some cases the same aspects allow us to use the LBC method to identify the order of a phase transition