Universal finite-size scaling functions for critical systems with tilted boundary conditions

We calculate finite-size scaling functions (FSSF’s) of Binder parameter g and magnetization distribution function $p\left(m\right)\mathrm{}$ for the Ising model on $L_1\times L_2$ square lattices with periodic boundary conditions in the horizontal $L_1$ direction and tilted boundary conditions in the vertical $L_2$ direction such that the $i\mathrm{th}$ site in the first row is connected with the $\mathrm{mod}{(i+cL}_1{,L}_1)\mathrm{th}$ site in the $L_2$ row of the lattice, where $1<~i<~L_1.$ For fixed sets of $\mathrm{}(a,c)\mathrm{}$ with ${a=L}_1{/L}_2,$ the FSSF’s of g and $p\left(m\right)\mathrm{}$ are universal and in such cases ${a/(c}^2{a}^2+1)$ is an invariant. For percolation on lattices with fixed a, the FSSF of the existence probability (also called spanning probability) is not affected by c.