Di Francesco et al.'s CFT - additional corrections to free-energy for strip geometries on a lattice? In classical spin systems, there's a nice way to extract the central charge of the model by looking at finite-size corrections to the free energy of strips of length $L$ and width $W$ in the limit of infinite length.
The book by Di Francesco, Mathieu, and Sénéchal, up to a change of notation, gives the following expressions for the free energy in periodic boundary conditions (pbc) and open boundary conditions (obc) on pages 140 and 421 respectively:
$$\lim_{L \to \infty} \frac{F_{pbc}}{LW} = f_0 - \frac{\pi c}{6 W^2}$$
$$\lim_{L \to \infty} \frac{F_{obc}}{LW} = f_0 - \frac{\pi c}{24 W^2}$$
Here, $c$ is the central charge.

For the 2d classical Ising model at the critical point, which is described at large distances with a CFT of $c=1/2$, I numerically find that the periodic boundary condition equation is asymptotically correct at large $W$, and I can rapidly extract the correct central charge. The corrections additional corrections appear to be $O(\frac{1}{W^3})$ or smaller.
However, for open boundary conditions, the free energy's behavior in $W$ looks quite different, and attempts to extract a central charge give a large negative value! It appears this is because the $\frac{\pi c}{24 W^2}$ piece is dominated by an additional finite-size correction of size $O(\frac{1}{W})$; including such a term in a fitting ansatz gives a more reasonable central charge.

This leads to my question. In general, when calculating $F_{pbc}$ and $F_{obc}$ for classical spins on a lattice, are there finite-size corrections in $W$ that asymptotically dominate the central charge $O(\frac{1}{W^2})$ term at large $W$? From the above, it looks like no for periodic boundary conditions and yes for open boundary conditions, but that might just be incidental to the 2d Ising model. If so, what are the forms of these corrections?
 A: According to this preprint, the free energy density of an infinite strip behaves as
$$f(W)=f(\infty)+{f_{\rm surf.}\over W}+{4\pi\over W^2}
  \left({c\over 24}-\Delta\right)
  +{\cal O}\left({1\over W^3}\right)$$
for Periodic Boundary Conditions and
$$f(W)=f(\infty)+{f_{\rm surf.}\over W}+{\pi\over W^2}
  \left({c\over 24}-\Delta\right)
  +{\cal O}\left({1\over W^3}\right)$$
for Open Boundary Conditions. $f_{\rm surf.}$ is the surface free energy and $\Delta$ the largest conformal weight. As far as I can remember, $f_{\rm surf.}$ is expected to be zero for the Ising model so no $1/W$ correction is expected for this model. You will definitely find more information in the paper (and the references).
Note that the strip is assumed to be infinite ($L\rightarrow +\infty$). Numerically, the free energy of an infinite strip can be estimated from the largest eigenvalue of the transfer matrix. It seems that you have data for finite strips of length $L$ (Monte Carlo simulations?). Then, I would advise you to have a look to the Schwartz-Christoffel mapping that will allow you to map your rectangular strip onto the complex upper half-plane.
