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The double-layer electron system with total filling factor $\nu=1/2$ can beregarded as two separate Fermi-liquid-like states with $\nu=1/4$ when the layerseparation is sufficiently large and there is no tunneling. The weak tunnelingin this state suffers an orthogonality catastrophe and it becomes irrelevant.Using the symmetric and antisymmetric combinations of layer indices as thepseudospin degrees of freedom, we show that there exists the first ordertransition from the above pseudospin unpolarized state to the pseudospinpolarized Fermi-liquid-like state with $\nu=1/2$ as the tunneling strengthbecomes sufficiently large.Comment: 4 page

Orthogonality catastrophe and spontaneous symmetry breaking in double-layer Fermi-liquid–like states