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For phase transitions in disordered systems, an exact theorem provides abound on the finite size correlation length exponent: \nu_{FS}<= 2/d. It isbelieved that the true critical exponent \nu of a disorder induced phasetransition satisfies the same bound. We argue that in disordered systems thestandard averaging introduces a noise, and a corresponding new diverging lengthscale, characterized by \nu_{FS}=2/d. This length scale, however, isindependent of the system's own correlation length \xi. Therefore \nu can beless than 2/d. We illustrate these ideas on two exact examples, with \nu < 2/d.We propose a new method of disorder averaging, which achieves a remarkablenoise reduction, and thus is able to capture the true exponents.Comment: 4 pages, Latex, one figure in .eps forma

physical review letters

Revisiting the Theory of Finite Size Scaling in Disordered Systems:<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">ν</mml:mi></mml:math>Can Be Less than<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>2</mml:mn><mml:mi>/</mml:mi><mml:mi mathvariant="italic">d</mml:mi></mml:math>

Revisiting the Theory of Finite Size Scaling in Disordered Systems:νCan Be Less than2/d