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The truncation scheme dependence of the exact renormalization group equations
is investigated for scalar field theories in three dimensions. The exponents
are numerically estimated to the next-to-leading order of the derivative
expansion. It is found that the convergence property in various truncations in
the number of powers of the fields is remarkably improved if the expansion is
made around the minimum of the effective potential. It is also shown that this
truncation scheme is suitable for evaluation of infrared effective potentials.
The physical interpretation of this improvement is discussed by considering
O(N) symmetric scalar theories in the large-N limit.Comment: 17 pages including 13 figures, LaTeX, to appear in Prog. Theor.
Phys., references adde
The non-perturbative Wegner-Roughton renormalization group is aiialyzed by the local potential approximation in O(N) scalar theories in d-dimensions (3sd:S4). The leading critical exponents 11 are calculated in order to investigate the effectiveness of the local potential approximation by comparing them with other non-perturbative methods. We show analytically that the local potential approximation gives the exact exponents 1,1p to O(E) in E-expansion and the leading in 1/N-expansion. We claim that this approximation offers fairly accurate results in the whole range of the parameter space of N and d. It is a great advantage of our method that no diverging expansions appear in the procedure.by guest on April 12, 2015
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