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 $p(m)$ for the Ising model on L₁×L₂ square lattices with periodic boundary conditions in the horizontal L₁ direction and tilted boundary conditions in the vertical L₂ direction such that the ith site in the first row is connected with the mod(i+cL₁,L₁)th site in the L₂ row of the lattice, where 1<~i<~L₁. For fixed sets of $(a,c)$ with a=L₁/L₂, the FSSF's of g and $p(m)$ are universal and in such cases a/(c²a²+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.