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Let us also suppose that <math>a</math> is positive and nonzero and <math>\beta</math> > <math>\alpha</math>. If <math>b</math> is zero, there is no stable equilibrium. If the [[scaling dimension]] of <math>\phi</math> is <math>c</math>, then the scaling dimension of <math>b</math> is <math>d-\beta c</math> where <math>d</math> is the number of dimensions. It is clear that if the scaling dimension of <math>b</math> is negative, <math>b</math> is an irrelevant parameter. However, the crucial point is the
:<math>\operatorname{VEV}\langle\phi\rangle=\left(\frac{a\alpha}{b\beta}\right)^{\frac{1}{\beta-\alpha}}=\left(\frac{a\alpha}{\beta}\right)^{\frac{1}{\beta-\alpha}}b^{-\frac{1}{\beta-\alpha}}</math>.
depends very sensitively upon <math>b</math>, at least for small values of <math>b</math>. Because the nature of the IR physics also depends upon the <math>\mathrm{VEV}</math>, the IR physics looks very different even for a tiny change in <math>b</math> not because the physics in the vicinity of <math>\phi=0</math> changes much -- it hardly changes at all -- but because the <math>\mathrm{VEV}</math> we are expanding about has changed enormously.
In [[supersymmetry|supersymmetric]] models with a [[moduli|modulus]], we can often have dangerously irrelevant parameters.
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