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We analyze the lateral critical Casimir force acting between two planar,chemically inhomogeneous walls confining an infinite 2D Ising strip of width$M$. The inhomogeneity of each of the walls has size $N_1$; they are shifted bythe distance $L$ along the strip. Using the exact diagonalization of thetransfer matrix, we calculate the lateral critical Casimir force and discussits properties, in particular its scaling close to the 2D bulk critical point,as a function of temperature, surface magnetic field, and the geometricparameters $M$, $N_1$, $L$. We determine the magnetization profiles whichdisplay the formation of the bridge joining the inhomogeneities on the wallsand establish the relation between the characteristic properties of the lateralCasimir force and magnetization morphologies. We check numerically thatbreaking of the bridge is related to the inflection point of the lateral force.

Lateral critical Casimir force in 2D Ising strip with inhomogeneous walls