### Universality class

Singular behaviors of physical properties around the phase transition point are governed by a few parameters (these parameters are called critical exponents) and the combination of the critical exponents is called universality class. Symmetries and spatial dimensions of the system determine the universality class and details of the system such as strength of interactions and the lattice structures do not change universality class. To determine the universality class of the phase transitions, it is necessary to perform the high-accuracy calculations such as the unbiased Monte Carlo calculations. Unbiased Monte Carlo calculations can be done with ALPS or DSQSS and the estimation of the critical exponents from the numerical data can be done with BSA.

### Variational Monte Carlo (VMC)

A method based on trial wave functions with parameters. By adjusting parameters according to variational principles one obtains optimal wave function. For the trial wave function for fermionic systems, a Slater determinant is often used with Gutzwiller-Jastrow type correlation factor to reflect correlation effects. Monte Carlo sapling is used in computing expectation values. Hence the name of the method. Because of the absence of the negative sign problem, this method is applicable to a broad range of problems including the first principles calculation (e.g., CASINO), quantum chemistry (e.g., QWalk), lattice fermion systems (e.g., mVMC), etc.

### X-ray spectroscopy analysis

When one irradiates some material with X-ray, the component of X-ray spectrum corresponding to the excitation of the inner shell of an atom contained in the material is absorbed. The fine structure in the spectrum of this X-ray absorption edge is called X-ray absorption fine structure (XAFS), and contains various information on the structure of the material in the atomistic scale. To extract such information, it is necessary to compute the anticipated electronic state of the related atoms and compare it with experiments. Most of applications for X-ray analysis, such as FEFF, Demeter and Missing, come with functions that produce X-ray absorption spectrum, so that the comparison to experiments can be done easily. In addition, by using packages of first-principles calculation with X-ray spectrum calculation capability (e.g., WIEN2k, Exciting, Quantum ESPRESSO, ANINIT, AkaiKKR SPRKKR GPAW) one can do the X-ray analysis in higher precision.