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Crossover scaling between dynamic universality classes implies a link between the dynamic exponents of the two and the crossover exponents at the unstable process. I named this the ztheorem .This property is especially useful when the crossover field is a a redundant stress tensor type operator for the stable process and the unstable one has known scaling properties, such that its dynamic exponent and the crossover exponent are known exactly. An example is the crossover between EdwardsWilkinson and KPZ type growth. In 1D, the KPZ dynamic exponent is therefore simply equal to z(KPZ)=z(EW)y(cr)=20.5=1.5. In higher dimensions this does not work, because EW growth becomes stable and an intermediate unstable fixed point separates it from KPZ growth. 
D dimensional dynamic processes that can be formulated as Master equations are intrinsically related to time evolution operators in quantum field theory and transfer matrices of D+1 equilibrium statistical mechanics.One example of this equivalence is the exact mapping between 1D KPZ growth and facetridge endpoints in 2D equilibrium crystal shapes .


spinhalf quantum chain phase diagrampercolation cluster 