Machine Learning as a universal tool for quantitative investigations of phase transition

Understand

The problem of identifying the phase of a given system for a certain value of the temperature can be reformulated as a classification problem in Machine Learning.

• Taking as a prototype the Ising model and using the Support Vector Machine as a tool to classify Monte Carlo generated configurations, we show that the critical region of the system can be clearly identified and the symmetry that drives the transition can be reconstructed from the performance of the learning process.
• The role of the discrete symmetry of the system in obtaining this result is discussed.
• A finite size analysis of the learned Support Vector Machine decision function allows us to determine the critical temperature and critical exponents with a precision that is comparable to that of the most efficient numerical approaches relying on a known Hamiltonian description of the system.