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.
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.