# How do I calculate the acceptance criterion for configuration bias sampling of my polymer?

I am running a lattice simulation of a single chain polymer on a lattice with every other site occupied by solvent. The additional wrinkle is that every particle on the lattice has a number/spin orientation associated with it, which is subject to change throughout the simulation. There are $$Z$$ spins possible for every particle. The range of interaction is a nearest-neighbor interaction. Two particles cannot occupy the same site. \begin{align} &\mathcal{H} = \sum _{(i,j)} \epsilon _{ij} \\ &\epsilon_{ij} = \begin{cases} \epsilon ^a, \text{ if spins at locations i, j are the same }\\ \epsilon^n, \text{ if spins at locations i, j spins are not the same} \end{cases} \end{align} where $$(i,j)$$ are two lattice sites which are nearest neighbor to one another. Once I plant a polymer on such a lattice and fill up every other site on the lattice with solvent, I want to sample this system. How do I perform polymer configuration moves, such as configurational bias chain regrowth (CBCR)? This is how I would run CBCR if I did not have solvent:

1. Pick a uniformly random monomer on the chain.
2. Pick a side where you want to regrow polymer.
3. Regrow polymer one monomer at a time. Calculate all the possible energetic states of the monomer per Rosenbluth sampling.
4. Include Rosenbluth weights in acceptance criterion.

But how do I do this type of regrowth if I have a lattice full of solvent? Every time I go to a new spot, I have to displace a solvent molecule. How do I account for the fact that every move involves some sort of solvent displacement. If required, I can give more explanation of the system I am performing.

I would appreciate any advice you have for me!

From there you can just do standard lattice statistical mechanics. How does a solvent-ed site "feel" about being next to other solvent-ed sites? Next to polymer sites? Being flipped into a polymer site? Well, all those will be encoded in $$\epsilon_{ij}$$ neighbour terms and $$\mu_i$$ field terms. If your terms are well-chosen, you should have a reasonable model.