[challenge]: Use neural network to represent renormalized Hamiltonians for classical spin systems

Released by

Yantao Wu, Institute of Physics, CAS

Contact email

yantaow@iphy.ac.cn

Method

Monte Carlo sampling, variational calculation, renormalization group
Reference: Phys. Rev. Lett. 119, 220602, 2017. [arXiv:1707.08683]

Challenge issue

The variational Monte Carlo Renormalization Group (VMCRG) kills two birds with one stone: 1. It variationally obtains the renormalized Hamiltonian given the RG prescription; 2. During the variational calculation, it cures the sampling difficulty of the underlying system, for example, the critical slowing down at the phase transition point and, more seriously, the relaxation slow down in a spin glass.

The RG needs to be performed for many iterations, and a variational bias is introduced at each iteration due to the ansatz for the renormalized Hamiltonian has limited representability. The renormalized Hamiltonians in MCRG are traditionally represented with nearest neighbor couplings, next nearest neighbor couplings, etc. Now we want to use the more expressive neural networks to represent them.

Easy goal: successful in 2D Ising model at 45x45.

Hard goal: successful in 3D spin glass at 45x45x45, to determine the spin glass transition point. This is considered to be an extremely difficult task in classical computational statistical mechanics.

No files, tests, or entry points are named. Start by inspecting the repository's Python structure and any existing Monte Carlo or renormalization-group code, then determine how a neural network could represent the renormalized Hamiltonian. Done means achieving the stated 2D Ising model goal; the 3D spin-glass goal is explicitly described as extremely difficult.