Abstract
We derive an approximate renormalization group (RG) flow equation for the local effective potential of single-component ${\ensuremath{\varphi}}^{4}$ field theory at finite temperature. Previous zero-temperature RG equations are recovered in the low- and high-temperature limits, in the latter case, via the phenomenon of dimensional reduction. We numerically solve our RG equations to obtain local effective potentials at finite temperature. These are found to be in excellent agreement with Monte Carlo results, especially when lattice artifacts are accounted for in the RG treatment.
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