Is the Ground State Energy of the Two-Dimensional XX Model Known?

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I am curious about XX model with quantum 1/2-spins in two dimensions. Is ground state energy for this model known? I was not able to find numerical or theoretical results in electronical archives.
 
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Jordan-wigner transformation is useful for 1/2 spin system
i don't remember the Hamiltonian of xx model, but for 2 d system, seems difficult to sovle it exactly.
some numerical methods, like lanczos algorithm ,VMC...
try some old archives in prl and prb at 1980s...
 
to yuanyuan5220, thanks for your message.
Really, Jordan-Wigner transformation in one-dimensional case reduces the XX model to free fermions model, which is exactly solvable. In two dimensions it doesn't work. Can you explain to me what is "old archives in prl and prb at 1980s", please?
 

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