Feynman-Graph Expansion for the Equation of State near the Critical Point

Brézin, E.; Wallace, D. J.; Wilson, Kenneth G.

doi:10.1103/physrevb.7.232

Cited by 243 publications

(117 citation statements)

References 13 publications

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“…The calculation of scaling functions and critical exponents has been a very important application of the Renormalization Group. First determinations of the scaling function for the order parameter or the magnetic equation of state have been obtained from perturbative RG methods, such as the ε-expansion [249,250,251].…”

Section: ∂M ∂Hmentioning

confidence: 99%

Modeling finite-volume effects and chiral symmetry breaking in two-flavor QCD thermodynamics

Klein

2017

Physics Reports

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Finite-volume effects in Quantum Chromodynamics (QCD) have been a subject of much theoretical interest for more than two decades. They are in particular important for the analysis and interpretation of QCD simulations on a finite, discrete space-time lattice. Most of these effects are closely related to the phenomenon of spontaneous breaking of the chiral flavor symmetry and the emergence of pions as light Goldstone bosons. These long-range fluctuations are strongly affected by putting the system into a finite box, and an analysis with different methods can be organized according to the interplay between pion mass and box size. The finite volume also affects critical behavior at the chiral phase transition in QCD. In the present review, I will be mainly concerned with modeling such finite volume effects as they affect the thermodynamics of the chiral phase transition for two quark flavors.I review recent work on the analysis of finite-volume effects which makes use of the quark-meson model for dynamical chiral symmetry breaking. To account for the effects of critical long-range fluctuations close to the phase transition, most of the calculations have been performed using non-perturbative Renormalization Group (RG) methods. I give an overview over the application of these methods to a finite volume. The method, the model and the results are put into the context of related work in random matrix theory for very small volumes, chiral perturbation theory for larger volumes, and related methods and approaches. They are applied towards the analysis of finite-volume effects in lattice QCD simulations and their interpretation, mainly in the context of the chiral phase transition for two quark flavors.

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Section: ∂M ∂Hmentioning

confidence: 99%

Modeling finite-volume effects and chiral symmetry breaking in two-flavor QCD thermodynamics

Klein

2017

Physics Reports

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“…the critical T * , p * and n * for the liquid-gas transition -is measured quite precisely. The approach to criticality is governed by universal [140] and mean field results are denoted by "ǫ" and "mf ", respectively. Apart from our results the curves are taken from ref.…”

Section: Gas-liquid Transition and The Ising Universality Class 36mentioning

confidence: 99%

Non-perturbative renormalization flow in quantum field theory and statistical physics

2002

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We review the use of an exact renormalization group equation in quantum field theory and statistical physics. It describes the dependence of the free energy on an infrared cutoff for the quantum or thermal fluctuations. Non-perturbative solutions follow from approximations to the general form of the coarse-grained free energy or effective average action. They interpolate between the microphysical laws and the complex macroscopic phenomena. Our approach yields a simple unified description for O(N )-symmetric scalar models in two, three or four dimensions, covering in particular the critical phenomena for the second-order phase transitions, including the Kosterlitz-Thouless transition and the critical behavior of polymer chains. We compute the aspects of the critical equation of state which are universal for a large variety of physical systems and establish a direct connection between microphysical and critical quantities for a liquid-gas transition. Universal features of first-order phase transitions are studied in the context of scalar matrix models. We show that the quantitative treatment of coarse graining is essential for a detailed estimate of the nucleation rate. We discuss quantum statistics in thermal equilibrium or thermal quantum field theory with fermions and bosons and we describe the high temperature symmetry restoration in quantum field theories with spontaneous symmetry breaking. In particular we explore chiral symmetry breaking and the high temperature or high density chiral phase transition in quantum chromodynamics using models with effective four-fermion interactions.This work is dedicated to the 60th birthday of Franz Wegner. *

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“…The equation of state is clearly a rotation symmetry-breaking one. But if H (x) is normalized at the values x = 0 and x = −1 such that H = M δ and H = 0, respectively, where x = t (g * M 2 ) −1/2β , the rotation symmetry-breaking and f (2) factors disappear and it assumes its well-known universal form [25]. Now we proceed by evaluating the minimal set of amplitude ratios.…”

Section: Amplitude Ratios In Normalization Conditions Schemementioning

confidence: 99%

Probing the two-scale-factor universality hypothesis by exact rotation symmetry-breaking mechanism

et al. 2017

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We probe the two-scale-factor universality hypothesis by evaluating, firstly explicitly and analytically at the one-loop order, the loop quantum corrections to the amplitude ratios for O(N ) λφ 4 scalar field theories with rotation symmetry breaking in three distinct and independent methods in which the rotation symmetry-breaking mechanism is treated exactly. We show that the rotation symmetrybreaking amplitude ratios turn out to be identical in the three methods and equal to their respective rotation symmetrybreaking ones, although the amplitudes themselves, in general, depend on the method employed and on the rotation symmetry-breaking parameter. At the end, we show that all these results can be generalized, through an inductive process based on a general theorem emerging from the exact calculation, to any loop level and physically interpreted based on symmetry ideas.

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Feynman-Graph Expansion for the Equation of State near the Critical Point

Cited by 243 publications

References 13 publications

Modeling finite-volume effects and chiral symmetry breaking in two-flavor QCD thermodynamics

Modeling finite-volume effects and chiral symmetry breaking in two-flavor QCD thermodynamics

Non-perturbative renormalization flow in quantum field theory and statistical physics

Probing the two-scale-factor universality hypothesis by exact rotation symmetry-breaking mechanism

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