Resummation in hot field theories

There has been significant progress in our understanding of finite-temperature field theory over the past decade. In this paper, we review the progress in perturbative thermal field theory focusing on thermodynamic quantities. We first discuss the breakdown of naive perturbation theory at finite temperature and the need for an effective expansion that resums an infinite class of diagrams in the perturbative expansion. This effective expansion which is due to Braaten and Pisarski, can be used to systematically calculate various static and dynamical quantities as a weak-coupling expansion in powers of g. However, it turns out that the weak-coupling expansion for thermodynamic quantities are useless unless the coupling constant is very small. We critically discuss various ways of reorganizing the perturbative series for thermal field theories in order to improve its convergence. These include screened perturbation theory (SPT), hard-thermal-loop perturbation theory, the Φ-derivable approach, dimensionally reduced (DR) SPT, and the DR Φ-derivable approach.     

A Brief Overview of Hard-Thermal-Loop Perturbation Theory

The poor convergence of quantum field theory at finite temperature has been one of the main obstacles in the practical applications of thermal QCD for decades.Here we briefly review the progress of hard-thermal-loop perturbation theory (HTLpt) in reorganizing the perturbative expansion in order to improve the convergence.The quantum mechanical anharmonic oscillator is used as a simple example to show the breakdown of weak-coupling expansion,and variational perturbation theory is introduced as an effective resummation scheme for divergent weak-coupling expansions.We discuss HTLpt thermodynamic calculations for QED,pure-glue QCD,and QCD with N f=3 up to three-loop order.The results suggest that HTLpt provides a systematic framework that can be used to calculate both static and dynamic quantities for temperatures relevant at LHC.     

Fluctuations and the energy-optimal control of chaos

We compute the pressure of a finite-density quark-gluon plasma at zero temperature to leading order in hard-thermal-loop perturbation theory, which includes the fermionic excitations and Landau damping. The result is compared with the weak-coupling expansion for finite positive chemical potential &mgr; through order alpha(2)(s) and with a quasiparticle model with a mass depending on &mgr;.     

Study of the gluon propagator in the large-Nf limit at finite temperature and chemical potential for weak and strong couplings

At finite temperature and chemical potential, the leading-order (hard-thermal-loop) contributions to the gauge-boson propagator lead to momentum-dependent thermal masses for propagating quasiparticles as well as dynamical screening and Landau damping effects. We compare the hard-thermal-loop propagator with the complete large-N_f gluon propagator, for which the usually subleading contributions, such as a finite width of quasiparticles, can be studied at nonperturbatively large effective coupling. We also study quantitatively the effect of Friedel oscillations in low-temperature electrostatic screening.     

Thermodynamic properties of a hard-core Lennard-Jones fluid from computer simulation and the coupling parameter series expansion

ABSTRACT

The thermodynamic properties of a fluid with an interaction potential consisting in a hard-sphere core plus a Lennard-Jones tail have been obtained by Monte Carlo (MC) NVT simulation as a function of the density along several isotherms. In addition, the liquid–vapour coexistence has been determined by means of histogram-reweighting MC. These data have been used to analyse the performance of perturbation theory. To this end, the first three perturbation terms of the inverse temperature expansion of the Helmholtz free energy have been obtained by means of MC NVT simulations to test the convergence of the perturbation series and to compare with the predictions of the coupling parameter series expansion. Then, the predictions of the latter theory for the thermodynamic properties have been compared with the simulations, revealing the overall excellent performance of this perturbation theory for this model fluid, except in the vicinity of the critical point.     

The generalized van Laar approximation for free energy

The van Laar equation for the uniform substance phase is analyzed. Based on this, an expression for free energy is found. The structure of the expression allowed us to create a method for determining the free energy in an arbitrary order of the perturbation theory. A generalized equation for free energy is derived based on the using thermodynamic perturbation theory and the accelerated method of convergence of the series of the perturbation theory. This expression agrees well with the asymptotic behavior of the free energy and with the known experimental data. It can be successfully used to describe the behavior of the substance in a super-critical region, as well as to investigate the metastable phase. It is shown that the expression for free energy can be used for a broad class of substances.     

Comparing different hard-thermal-loop approaches to quark number susceptibilities

We compare our previously proposed hard-thermal-loop (HTL) resummed calculation of quark number susceptibilities using a self-consistent two-loop approximation to the quark density with a recent calculation of the same quantity at the one-loop level in a variant of HTL-screened perturbation theory. Besides pointing out conceptual problems with the latter approach, we show that it severely over-includes the leading-order interaction effects, while including none of the plasmon terms, which is the main reason for requiring improved resummation schemes. Received: 27 June 2002 / Revised version: 23 September 2002 / Published online: 31 January 2003     

NNLO hard-thermal-loop thermodynamics for QCD

We calculate the thermodynamic functions of a quark–gluon plasma for general Nc$N_c$ and Nf$N_f$ to three-loop order using hard-thermal-loop perturbation theory. At this order, all the ultraviolet divergences can be absorbed into renormalizations of the vacuum, the HTL mass parameters, and the strong coupling constant. We show that at three loops, the results for the pressure and trace anomaly are in very good agreement with recent lattice data down to temperatures T∼2Tc$T\sim 2T_c$.     

Phase transition and thermodynamic stability in extended phase space and charged Hořava–Lifshitz black holes

For charged black holes in Ho?ava–Lifshitz gravity, a second order phase transition takes place in extended phase space where the cosmological constant is taken as thermodynamic pressure. We relate the second order nature of phase transition to the fact that the phase transition occurs at a sharp temperature and not over a temperature interval. Once we know the continuity of the first derivatives of the Gibbs free energy, we show that all the Ehrenfest equations are readily satisfied. We study the effect of the perturbation of the cosmological constant as well as the perturbation of the electric charge on thermodynamic stability of Ho?ava–Lifshitz black hole. We also use thermodynamic geometry to study phase transition in extended phase space. We investigate the behavior of scalar curvature of Weinhold, Ruppeiner, and Quevedo metric in extended phase space of charged Ho?ava–Lifshitz black holes. It is checked if these curvatures could reproduce the result of specific heat for the phase transition.     

An adaptation of the lattice gas to the water problem. II. Second-order approximation

The adaptation of the lattice-gas model to embody features possessed by water is further explored. On the basis of Martin's functional derivative formulation of Ising problems, a perturbation scheme is developed which allows calculation of the free energy to any desired order in the interaction potential at fixed density. The free energy correct to second order in the interaction strength is utilized here for calculation of other thermodynamic properties of the model. With reasonable choices of values of the interaction parameters these thermodynamic properties of the model can be brought into agreement with those of real water.     

First-Order mansition in a Quantum Ising Model with p-Spin Interactions and a Random Field

We study a quantum transverse Ising model with pspin interactions in the presence of a random field. The formulation for the free energy of the system is derived by making use of the Suzuki-Trotter approach with the thermodynamic perturbation theory, and the first-order transitions are obtained in the limit p→∞.     

Functional Integrals and Free Energy in sine-Gordon-Thirring Model with Impurity Coupling

The free energy at low temperature in 1D sine-Gordon-Thirring model with impurity coupling is studied by means of functional integrals method. For massive free sine-Gordon-Thirring model, free energy is obtained from perturbation expansion of functional determinant. Moreover, the free energy of massive model is calculated by use of an auxiliary Bose field method.     

Phase transition in liquid crystal elastomers—A Monte Carlo study employing non-Boltzmann sampling

We investigate nematic-isotropic transition in liquid crystal elastomers employing a variant of Wang-Landau sampling. This technique facilitates calculation of the density of states from which other thermodynamic properties can be obtained. We consider a lattice model of a liquid crystal elastomer and a Hamiltonian which accounts for interactions among liquid crystalline units and interaction of local nematics with global strain. We investigate the effect of varying the strength of coupling between nematic and orientational degrees of freedom. When the local director is coupled strongly to the global strain, the transition is strongly first order. When the strength of the coupling decreases the transition becomes weakly first order. The transition temperature decreases when the coupling becomes weaker. We also report for the first time results on variation of free energy as a function of average energy at different temperatures and coupling constants.     

LJ模型的热力学特性、相平衡及用于真实分子的研究

结合描述硬球固体Helmholtz自由能的自由体积方法与描述硬球固体径向分布函数的拟合的分析表达式与一阶热力学摄动理论,用于描述Lennard Jones(LJ)固体的Helmholtz自由能.按照一个修正的WCA方法将LJ势分为短程排斥部分与长程吸引部分,将文献中一个用于求取液相的等价的硬球直径的简单的迭代法扩展到固相,用于求取固相的等价的硬球直径.在固体Helmholtz自由能的计算中,使用200壳层,以便获得精确的结果.体相LJ液体的热力学特性由一个最近提出的状态方程求取.该方法很好地描述了LJ固体的过量Helmholtz自由能与状态方程,满意地描述了Lennard Jones模型的相平衡;通过选取合适的LJ势参数,能很好地描述了真实分子的融化曲线.     

Band structure and thermodynamic potentials

The behavior of different thermodynamic functions of a system of delocalized electrons in a crystal is considered in the single-band strong coupling approximation depending on the degree of energy band filling and temperature. The chemical potential, grand thermodynamic potential, internal energy, free energy, entropy, and heat capacity are numerically calculated. Dependences of these quantities on the electron concentration at high temperatures are investigated. Their limited energy spectrum leads to the special features in the behavior of these quantities in comparison with the free electron gas.     

Pertubation theory for systems with strong short-ranged interactions

We propose a variant of thermodynamic perturbation theory based on the Mayer f-function which is applicable to strongly repulsive, and even singular interactions. The expansion of the free energy is successfully tested against known ‘exact results’ for hard-sphere fluids, and then applied to binary mixtures of particles with non-additive hard cores or shouldered potentials. The resulting phase diagrams agree well with existing simulation data and theoretical predictions.     

An Orbital‐Free Quantum Hypernetted Chain Model Based Perturbation Theory for Equation of State of Hydrogen and Helium in Warm Dense Regime

We present in this work, a thermodynamic perturbation theory for equation of state of hydrogen and helium in the warm dense regime. The system is modeled as a mixture of classical point ions and quantum electrons. A perturbation series for Helmholtz free energy and correlation functions of the ions and electrons as a function of density and temperature is proposed. Combining the classical thermodynamic perturbation theory and the orbitial‐free quantum hyper‐netted chain theory, a systematic procedure to obtain the terms of the perturbation series is developed. The ion‐ion correlations are treated within the hyper‐netted chain approximation and the ion‐electron correlations are treated within the Thomas‐Fermi‐Dirac‐Weizsäcker approximation. The method has been applied to obtain isotherms of hydrogen and helium in the warm dense regime. The isotherms are compared with available ab‐initio data and the results are analyzed. A good agreement with ab‐initio data has been observed for pressures greater than one Mbar. Advantages and limitations of the present method are discussed along with possible future improvements. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Perturbative study of thermodynamic properties for the two-leg spin ladder

We apply finite-temperature perturbation theory to study thermodynamic properties of the two-leg antiferromagnetic spin ladder in the strong interchain coupling limit. The internal energy, specific heat and uniform susceptibility are calculated analytically by third-order perturbation expansions. At zero temperature, the present method results in the same ground state energy as that obtained by the strong coupling expansion without temperature. At finite-temperature, we obtain a peak in the specific heat and a broad maximum in the uniform susceptibility. The results agree quite well with experimental data for the material Cu₂(C₅H₁₂N₂)₂Cl₄ and the numerical data of 8-order series expansion theory.     

Theoretical investigations on the structural, lattice dynamical and thermodynamic properties of XC (X=Si, Ge, Sn)

First-principles calculations, which is based on the plane-wave pseudopotential approach to the density functional perturbation theory within the local density approximation, have been performed to investigate the structural, lattice dynamical, and thermodynamic properties of SiC, GeC, and SnC. The results of ground state parameters, phase transition pressure and phonon dispersion are compared and agree well with the experimental and theoretical data in the previous literature. The obtained phonon frequencies at the zone-center are analyzed. We also used the phonon density of states and quasiharmonic approximation to calculate and predict some thermodynamic properties such as entropy, heat capacity, internal energy, and phonon free energy of SiC, GeC, and SnC in B3 phase.