Almost second order phase transitions

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Abstract
We investigate models which have more than one coupling constant and which have no (codimension one) fixed point in the renormalization group flow in an ε=4-d expansion. We show that the pseudocritical behavior of these systems is dominated by a minimum in the flow. By using the local potential approximation of the renormalization group, the properties of such minima are described. If a minimum is ‘‘good enough,’’ it can fake a fixed point, but there are corrections to the relation between the exponents. Finally, we show that similar results hold in an ε expansion.