Second-order and fluctuation-induced first-order phase transitions with functional renormalization group equations

Abstract

We investigate phase transitions in scalar field theories using the functional renormalization group (RG) equation. We analyze a system with U(2) × U(2) symmetry, in which there is a parameter λ2 that controls the strength of the first-order phase transition driven by fluctuations. In the limit of λ2 → 0, the U(2) × U(2) theory is reduced to an O(8) scalar theory that exhibits a secondorder 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 λ2 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.

Chiral symmetry breaking patterns in theUL(n)×UR(n)meson model

“…The nonexistence of an infrared stable fixed point indirectly shows a transition, which (if exists) is fluctuation induced, and of first order. This has been confirmed numerically for the n = 2 case with the use of the functional renormalization group (FRG) approach [21][22][23], and expected to remain true at n > 2.…”

“…This is expected to be a good approximation if the anomalous dimension remains small. With the choice of the commonly used regulator function introduced by Litim [31]: (23), in 3+1 dimensions we get…”

Functional renormalization for chiral andUA(1)symmetries at finite temperature

“…In chiral limit, the condensateσ 8 disappears and the flow equation for the condensateσ 0 is decoupled from the others and can be analytically solved as (28). The evolutions ofσ 0k at different temperature is shown in Fig.8.…”

“…In this case, all the mesons become degenerate with mass m 2 and their contributions to the flow equation are the same. The procedure for the SU (2) model is discussed in [25,28].…”

“…In this work we use the functional renormalization group (FRG) method to study the chiral symmetry and U A (1) symmetry in the SU (3) linear sigma model at finite temperature. As a non-perturbative method [18][19][20], the FRG has been used to study phase transitions in various systems like cold atom gas [21], nucleon gas [22] and hadron gas [23][24][25][26][27][28]. By solving the flow equation which connects physics at different momentum scales, the FRG shows a great power to describe the phase transitions and the corresponding critical phenomena, which are normally difficult to be controlled in the mean field approximation because of the absence of the quantum fluctuations.…”