Second-order and Fluctuation-induced First-order Phase Transitions with
Functional Renormalization Group Equations
release_elptcxtzhvdivih7pdw6suthhq
by
Kenji Fukushima, Kazuhiko Kamikado, Bertram Klein
2011
Abstract
We investigate phase transitions in scalar field theories using the
functional renormalization group (RG) equation. We analyze a system with
U(2)xU(2) symmetry, in which there is a parameter λ_2 that controls the
strength of the first-order phase transition driven by fluctuations. In the
limit of λ_2→0, the U(2)xU(2) theory is reduced to an O(8) scalar
theory that exhibits a second-order phase transition in three dimensions. We
develop a new insight for the understanding of the fluctuation-induced
first-order phase transition as a smooth continuation from the standard RG flow
in the O(8) system. In our view from the RG flow diagram on coupling parameter
space, the region that favors the first-order transition emerges from the
unphysical region to the physical one as λ_2 increases from zero. We give
this interpretation based on the Taylor expansion of the functional RG
equations up to the fourth order in terms of the field, which encompasses the
ϵ-expansion results. We compare results from the expansion and from
the full numerical calculation and find that the fourth-order expansion is only
of qualitative use and that the sixth-order expansion improves the quantitative
agreement.
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