Crossover scaling functions from renormalization group trajectory integrals

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Abstract
We express the free energy of a system in its critical region as a line integral along a renormalization group trajectory. The kernal associated with the trajectory integral is just the spin independent part of the Hamiltonian generated by each renormalization group iteration. If the trajectory integral is parametrized in terms of nonlinear scaling fields, a closed expression for the crossover scaling function is obtained. Crossover scaling functions associated with free energy are calculated explicitly for recursion relation models treated by Riedel and Wegner, and the relevance to ε‐expansions near four dimensions is discussed. A breakdown of hyperscaling above the borderline dimensions (d=4 for critical points, and d=3 for tricritical points) arises naturally in the formalism.

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