This package includes a reference code of the new kernel method for the finite-size scaling analysis of critical phenomena. Please use a new command in the "CC2" folder.
The new method is based on the Gaussian process regression, which is called kernel method. After the advent of kernel methods in the machine learning community, the method of data analysis was drastically changed. Because the kernel method is very flexible for complex real data, the power of the kernel method can also help our scaling analysis.
The original paper [1] mainly considered the scaling law without corrections to scaling. The recent progress resolves the problem of corrections to scaling systematically [2]. In fact, this reference code can deal with a general finite-size scaling law with or without corrections to scaling as follows:
\begin{equation} A(T, L) = L^{c_2} F[ ( T - T_c ) L^{c_1} ], \end{equation}and
\begin{equation} A(T, L) = L^{c_2} \left(F[ ( T - T_c ) L^{c_1} ] + G[ ( T - T_c ) L^{c_1} ] L^{-c_3} \right), \end{equation}where \( A \) is an observable, \(L\) is a system size, \(T_c\) is a critical point, and \(c_3 > 0\) is an irrelevant critical exponent.
Because we assume only the smoothness of the functions \( F \) and \( G \), we do not need to limit the range of data near a critical point so that the scaling function is approximated by a polynomial. Thus, this code can be widely applied to real data in critical phenomena(see the 2nd demo in this page). This code also uses a hybrid Monte Carlo to estimate the confidential intervals of inferred values.
I recommend this code for all users of the finite-size scaling analysis, because it is very flexible, and it automatically and easily can estimates the values of critical exponents and a critical point without the technical knowledge. If this new method is useful to your study, I hope that you cite my papers to spread this new method.
July, 2015
Kenji Harada
This folder includes a new command of Bayesian finite size scaling.
This folder includes an old command of Bayesian finite size scaling.
An implementation with PyTorch (python) of two FSS methods by using Gaussian process (GP) and a neural network (NN).