Low Temperature Surface Spin-Glass Transition in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">γ</mml:mi></mml:math>-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Fe</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>Nanoparticles

$\ensuremath{\gamma}\ensuremath{-}{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}$ magnetic nanoparticles, with a very high surface to volume ratio, exhibit both strong exchange anisotropy and magnetic training effect. At the same time high field irreversibility in $M\left(H\right)$ curves and zero field cooled--field cooled (ZFC-FC) processes has also been detected. A low temperature spin-glass-like transition is evidenced at ${T}_{F}\ensuremath{\approx}42\mathrm{K}$ with strong irreversibility even at $H\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}55\mathrm{kOe}$. ${T}_{F}\left(H\right)$ evolves following the well known de Almeida--Thouless line $\ensuremath{\delta}{T}_{F}\ensuremath{\propto}{H}^{2/3}$. The thermal dependence of the exchange anisotropy field ${H}_{E}$ is described by the random-field model of exchange anisotropy. In the framework of this theory, a surface spin-glass layer about 0.6 nm thick is determined.